/// @brief Monte Carlo Integrator /// /// @callgraph /// @callergraph /// /// @details Integrates the system using a Monte Carlo solver with tuned step width /// /// @section License /// Use of this code, either in source or compiled form, is subject to license from the authors. /// Copyright \htmlonly © \endhtmlonly Richard Evans, 2009-2011. All Rights Reserved. /// /// @section Information /// @author Richard Evans, [email protected] /// @version 1.0 /// @date 05/02/2011 /// /// @return EXIT_SUCCESS /// /// @internal /// Created: 05/02/2011 /// Revision: --- ///===================================================================================== /// int MonteCarlo(){ // Check for calling of function if(err::check==true) std::cout << "sim::MonteCarlo has been called" << std::endl; // calculate number of steps to calculate int nmoves = atoms::num_atoms; // Declare arrays for spin states std::valarray<double> Sold(3); std::valarray<double> Snew(3); // Temporaries int atom=0; double r=1.0; double Eold=0.0; double Enew=0.0; double DE=0.0; const int AtomExchangeType=atoms::exchange_type; // Material dependent temperature rescaling std::vector<double> rescaled_material_kBTBohr(mp::num_materials); std::vector<double> sigma_array(mp::num_materials); // range for tuned gaussian random move for(int m=0; m<mp::num_materials; ++m){ double alpha = mp::material[m].temperature_rescaling_alpha; double Tc = mp::material[m].temperature_rescaling_Tc; double rescaled_temperature = sim::temperature < Tc ? Tc*pow(sim::temperature/Tc,alpha) : sim::temperature; rescaled_material_kBTBohr[m] = 9.27400915e-24/(rescaled_temperature*1.3806503e-23); sigma_array[m] = rescaled_temperature < 1.0 ? 0.02 : pow(1.0/rescaled_material_kBTBohr[m],0.2)*0.08; } double statistics_moves = 0.0; double statistics_reject = 0.0; // loop over natoms to form a single Monte Carlo step for(int i=0;i<nmoves; i++){ // add one to number of moves counter statistics_moves+=1.0; // pick atom atom = int(nmoves*mtrandom::grnd()); // get material id const int imaterial=atoms::type_array[atom]; // Calculate range for move sim::mc_delta_angle=sigma_array[imaterial]; // Save old spin position Sold[0] = atoms::x_spin_array[atom]; Sold[1] = atoms::y_spin_array[atom]; Sold[2] = atoms::z_spin_array[atom]; // Make Monte Carlo move sim::mc_move(Sold, Snew); // Calculate current energy Eold = sim::calculate_spin_energy(atom, AtomExchangeType); // Copy new spin position atoms::x_spin_array[atom] = Snew[0]; atoms::y_spin_array[atom] = Snew[1]; atoms::z_spin_array[atom] = Snew[2]; // Calculate new energy Enew = sim::calculate_spin_energy(atom, AtomExchangeType); // Calculate difference in Joules/mu_B DE = (Enew-Eold)*mp::material[imaterial].mu_s_SI*1.07828231e23; //1/9.27400915e-24 // Check for lower energy state and accept unconditionally if(DE<0) continue; // Otherwise evaluate probability for move else{ if(exp(-DE*rescaled_material_kBTBohr[imaterial]) >= mtrandom::grnd()) continue; // If rejected reset spin coordinates and continue else{ atoms::x_spin_array[atom] = Sold[0]; atoms::y_spin_array[atom] = Sold[1]; atoms::z_spin_array[atom] = Sold[2]; // add one to rejection counter statistics_reject += 1.0; continue; } } } // Save statistics to sim namespace variable sim::mc_statistics_moves += statistics_moves; sim::mc_statistics_reject += statistics_reject; return EXIT_SUCCESS; }
///
/// @brief Runs the Constrained Monte Carlo algorithm
///
/// Chooses nspins random spin pairs from the spin system and attempts a
/// Constrained Monte Carlo move on each pair, accepting for either lower
/// energy or with a Boltzmann thermal weighting.
///
/// @return void
///
int ConstrainedMonteCarloMonteCarlo(){
// Check for calling of function
if(err::check==true) std::cout << "sim::ConstrainedMonteCarlo has been called" << std::endl;
// check for cmc initialisation
if(cmc::is_initialised==false) CMCMCinit();
int atom_number1;
int atom_number2;
int imat1;
int imat2;
double delta_energy1;
double delta_energy2;
double delta_energy21;
double Eold;
double Enew;
std::valarray<double> spin1_initial(3);
std::valarray<double> spin1_final(3);
double spin2_initial[3];
double spin2_final[3];
double spin1_init_mvd[3];
double spin1_fin_mvd[3];
double spin2_init_mvd[3];
double spin2_fin_mvd[3];
double M_other[3];
double Mz_old;
double Mz_new;
double sqrt_ran;
double probability;
// Material dependent temperature rescaling
std::vector<double> rescaled_material_kBTBohr(mp::num_materials);
std::vector<double> sigma_array(mp::num_materials); // range for tuned gaussian random move
for(int m=0; m<mp::num_materials; ++m){
double alpha = mp::material[m].temperature_rescaling_alpha;
double Tc = mp::material[m].temperature_rescaling_Tc;
double rescaled_temperature = sim::temperature < Tc ? Tc*pow(sim::temperature/Tc,alpha) : sim::temperature;
rescaled_material_kBTBohr[m] = 9.27400915e-24/(rescaled_temperature*1.3806503e-23);
sigma_array[m] = pow(1.0/rescaled_material_kBTBohr[m],0.2)*0.08;
}
const int AtomExchangeType=atoms::exchange_type; // Cast as constant and pass to energy calculation for speed
// save initial magnetisations
for(int mat=0;mat<mp::num_materials;mat++){
cmc::cmc_mat[mat].M_other[0] = 0.0;
cmc::cmc_mat[mat].M_other[1] = 0.0;
cmc::cmc_mat[mat].M_other[2] = 0.0;
}
for(int atom=0;atom<atoms::num_atoms;atom++){
int mat=atoms::type_array[atom];
cmc::cmc_mat[mat].M_other[0] += atoms::x_spin_array[atom]; //multiplied by polar_vector below
cmc::cmc_mat[mat].M_other[1] += atoms::y_spin_array[atom];
cmc::cmc_mat[mat].M_other[2] += atoms::z_spin_array[atom];
}
// make a sequence of Monte Carlo moves
for (int mcs=0;mcs<atoms::num_atoms;mcs++){
// Randomly select spin number 1
atom_number1 = int(mtrandom::grnd()*atoms::num_atoms);
imat1=atoms::type_array[atom_number1];
sim::mc_delta_angle=sigma_array[imat1];
// check for constrained or unconstrained
if(mp::material[imat1].constrained==false){
// normal MC
// Save old spin position
spin1_initial[0] = atoms::x_spin_array[atom_number1];
spin1_initial[1] = atoms::y_spin_array[atom_number1];
spin1_initial[2] = atoms::z_spin_array[atom_number1];
// Make Monte Carlo move
sim::mc_move(spin1_initial, spin1_final);
// Calculate current energy
Eold = sim::calculate_spin_energy(atom_number1, AtomExchangeType);
// Copy new spin position
atoms::x_spin_array[atom_number1] = spin1_final[0];
atoms::y_spin_array[atom_number1] = spin1_final[1];
atoms::z_spin_array[atom_number1] = spin1_final[2];
// Calculate new energy
Enew = sim::calculate_spin_energy(atom_number1, AtomExchangeType);
// Calculate difference in Joules/mu_B
delta_energy1 = (Enew-Eold)*mp::material[imat1].mu_s_SI*1.07828231e23; //1/9.27400915e-24
// Check for lower energy state and accept unconditionally
if(delta_energy1<0){
cmc::mc_success += 1.0;
}
// Otherwise evaluate probability for move
else{
if(exp(-delta_energy1*rescaled_material_kBTBohr[imat1]) >= mtrandom::grnd()){
cmc::mc_success += 1.0;
}
// If rejected reset spin coordinates and continue
else{
atoms::x_spin_array[atom_number1] = spin1_initial[0];
atoms::y_spin_array[atom_number1] = spin1_initial[1];
atoms::z_spin_array[atom_number1] = spin1_initial[2];
cmc::energy_reject += 1.0;
}
}
}
else{
// constrained MC move
const int imat=imat1;
// Save initial Spin 1
spin1_initial[0] = atoms::x_spin_array[atom_number1];
spin1_initial[1] = atoms::y_spin_array[atom_number1];
spin1_initial[2] = atoms::z_spin_array[atom_number1];
//spin1_init_mvd = matmul(polar_matrix, spin1_initial)
spin1_init_mvd[0]=cmc::cmc_mat[imat].ppolar_matrix[0][0]*spin1_initial[0]+cmc::cmc_mat[imat].ppolar_matrix[0][1]*spin1_initial[1]+cmc::cmc_mat[imat].ppolar_matrix[0][2]*spin1_initial[2];
spin1_init_mvd[1]=cmc::cmc_mat[imat].ppolar_matrix[1][0]*spin1_initial[0]+cmc::cmc_mat[imat].ppolar_matrix[1][1]*spin1_initial[1]+cmc::cmc_mat[imat].ppolar_matrix[1][2]*spin1_initial[2];
spin1_init_mvd[2]=cmc::cmc_mat[imat].ppolar_matrix[2][0]*spin1_initial[0]+cmc::cmc_mat[imat].ppolar_matrix[2][1]*spin1_initial[1]+cmc::cmc_mat[imat].ppolar_matrix[2][2]*spin1_initial[2];
// Make Monte Carlo move
sim::mc_move(spin1_initial, spin1_final);
//spin1_fin_mvd = matmul(polar_matrix, spin1_final)
spin1_fin_mvd[0]=cmc::cmc_mat[imat].ppolar_matrix[0][0]*spin1_final[0]+cmc::cmc_mat[imat].ppolar_matrix[0][1]*spin1_final[1]+cmc::cmc_mat[imat].ppolar_matrix[0][2]*spin1_final[2];
spin1_fin_mvd[1]=cmc::cmc_mat[imat].ppolar_matrix[1][0]*spin1_final[0]+cmc::cmc_mat[imat].ppolar_matrix[1][1]*spin1_final[1]+cmc::cmc_mat[imat].ppolar_matrix[1][2]*spin1_final[2];
spin1_fin_mvd[2]=cmc::cmc_mat[imat].ppolar_matrix[2][0]*spin1_final[0]+cmc::cmc_mat[imat].ppolar_matrix[2][1]*spin1_final[1]+cmc::cmc_mat[imat].ppolar_matrix[2][2]*spin1_final[2];
// Calculate current energy
Eold = sim::calculate_spin_energy(atom_number1, AtomExchangeType);
// Copy new spin position (provisionally accept move)
atoms::x_spin_array[atom_number1] = spin1_final[0];
atoms::y_spin_array[atom_number1] = spin1_final[1];
atoms::z_spin_array[atom_number1] = spin1_final[2];
// Calculate new energy
Enew = sim::calculate_spin_energy(atom_number1, AtomExchangeType);
// Calculate difference in Joules/mu_B
delta_energy1 = (Enew-Eold)*mp::material[imat1].mu_s_SI*1.07828231e23; //1/9.27400915e-24
// Compute second move
// Randomly select spin number 2 (i/=j) of same material type
atom_number2 = cmc::atom_list[imat1][int(mtrandom::grnd()*cmc::atom_list[imat1].size())];
imat2=atoms::type_array[atom_number2];
if(imat1!=imat2){
terminaltextcolor(RED);
std::cerr << "Error in MC/CMC integration! - atoms pairs are not from same material!" << std::endl;
terminaltextcolor(WHITE);
err::vexit();
}
// Save initial Spin 2
spin2_initial[0] = atoms::x_spin_array[atom_number2];
spin2_initial[1] = atoms::y_spin_array[atom_number2];
spin2_initial[2] = atoms::z_spin_array[atom_number2];
//spin2_init_mvd = matmul(polar_matrix, spin2_initial)
spin2_init_mvd[0]=cmc::cmc_mat[imat].ppolar_matrix[0][0]*spin2_initial[0]+cmc::cmc_mat[imat].ppolar_matrix[0][1]*spin2_initial[1]+cmc::cmc_mat[imat].ppolar_matrix[0][2]*spin2_initial[2];
spin2_init_mvd[1]=cmc::cmc_mat[imat].ppolar_matrix[1][0]*spin2_initial[0]+cmc::cmc_mat[imat].ppolar_matrix[1][1]*spin2_initial[1]+cmc::cmc_mat[imat].ppolar_matrix[1][2]*spin2_initial[2];
spin2_init_mvd[2]=cmc::cmc_mat[imat].ppolar_matrix[2][0]*spin2_initial[0]+cmc::cmc_mat[imat].ppolar_matrix[2][1]*spin2_initial[1]+cmc::cmc_mat[imat].ppolar_matrix[2][2]*spin2_initial[2];
// Calculate new spin based on constraint Mx=My=0
spin2_fin_mvd[0] = spin1_init_mvd[0]+spin2_init_mvd[0]-spin1_fin_mvd[0];
spin2_fin_mvd[1] = spin1_init_mvd[1]+spin2_init_mvd[1]-spin1_fin_mvd[1];
if(((spin2_fin_mvd[0]*spin2_fin_mvd[0]+spin2_fin_mvd[1]*spin2_fin_mvd[1])<1.0) && (atom_number1 != atom_number2)){
spin2_fin_mvd[2] = vmath::sign(spin2_init_mvd[2])*sqrt(1.0-spin2_fin_mvd[0]*spin2_fin_mvd[0] - spin2_fin_mvd[1]*spin2_fin_mvd[1]);
//spin2_final = matmul(polar_matrix_tp, spin2_fin_mvd)
spin2_final[0]=cmc::cmc_mat[imat].ppolar_matrix_tp[0][0]*spin2_fin_mvd[0]+cmc::cmc_mat[imat].ppolar_matrix_tp[0][1]*spin2_fin_mvd[1]+cmc::cmc_mat[imat].ppolar_matrix_tp[0][2]*spin2_fin_mvd[2];
spin2_final[1]=cmc::cmc_mat[imat].ppolar_matrix_tp[1][0]*spin2_fin_mvd[0]+cmc::cmc_mat[imat].ppolar_matrix_tp[1][1]*spin2_fin_mvd[1]+cmc::cmc_mat[imat].ppolar_matrix_tp[1][2]*spin2_fin_mvd[2];
spin2_final[2]=cmc::cmc_mat[imat].ppolar_matrix_tp[2][0]*spin2_fin_mvd[0]+cmc::cmc_mat[imat].ppolar_matrix_tp[2][1]*spin2_fin_mvd[1]+cmc::cmc_mat[imat].ppolar_matrix_tp[2][2]*spin2_fin_mvd[2];
//Calculate Energy Difference 2
// Calculate current energy
Eold = sim::calculate_spin_energy(atom_number2, AtomExchangeType);
// Copy new spin position (provisionally accept move)
atoms::x_spin_array[atom_number2] = spin2_final[0];
atoms::y_spin_array[atom_number2] = spin2_final[1];
atoms::z_spin_array[atom_number2] = spin2_final[2];
// Calculate new energy
Enew = sim::calculate_spin_energy(atom_number2, AtomExchangeType);
// Calculate difference in Joules/mu_B
delta_energy2 = (Enew-Eold)*mp::material[imat2].mu_s_SI*1.07828231e23; //1/9.27400915e-24
// Calculate Delta E for both spins
delta_energy21 = delta_energy1*rescaled_material_kBTBohr[imat1] + delta_energy2*rescaled_material_kBTBohr[imat2];
// Compute Mz_other, Mz, Mz'
Mz_old = cmc::cmc_mat[imat].M_other[0]*cmc::cmc_mat[imat].ppolar_vector[0] + cmc::cmc_mat[imat].M_other[1]*cmc::cmc_mat[imat].ppolar_vector[1] + cmc::cmc_mat[imat].M_other[2]*cmc::cmc_mat[imat].ppolar_vector[2];
Mz_new = (cmc::cmc_mat[imat].M_other[0] + spin1_final[0] + spin2_final[0]- spin1_initial[0] - spin2_initial[0])*cmc::cmc_mat[imat].ppolar_vector[0] +
(cmc::cmc_mat[imat].M_other[1] + spin1_final[1] + spin2_final[1]- spin1_initial[1] - spin2_initial[1])*cmc::cmc_mat[imat].ppolar_vector[1] +
(cmc::cmc_mat[imat].M_other[2] + spin1_final[2] + spin2_final[2]- spin1_initial[2] - spin2_initial[2])*cmc::cmc_mat[imat].ppolar_vector[2];
// Check for lower energy state and accept unconditionally
//if((delta_energy21<0.0) && (Mz_new>=0.0) ) continue;
// Otherwise evaluate probability for move
//else{
// If move is favorable then accept
probability = exp(-delta_energy21)*((Mz_new/Mz_old)*(Mz_new/Mz_old))*std::fabs(spin2_init_mvd[2]/spin2_fin_mvd[2]);
if((probability>=mtrandom::grnd()) && (Mz_new>=0.0) ){
cmc::cmc_mat[imat].M_other[0] = cmc::cmc_mat[imat].M_other[0] + spin1_final[0] + spin2_final[0] - spin1_initial[0] - spin2_initial[0];
cmc::cmc_mat[imat].M_other[1] = cmc::cmc_mat[imat].M_other[1] + spin1_final[1] + spin2_final[1] - spin1_initial[1] - spin2_initial[1];
cmc::cmc_mat[imat].M_other[2] = cmc::cmc_mat[imat].M_other[2] + spin1_final[2] + spin2_final[2] - spin1_initial[2] - spin2_initial[2];
cmc::mc_success += 1.0;
}
//if both p1 and p2 not allowed then
else{
// reset spin positions
atoms::x_spin_array[atom_number1] = spin1_initial[0];
atoms::y_spin_array[atom_number1] = spin1_initial[1];
atoms::z_spin_array[atom_number1] = spin1_initial[2];
atoms::x_spin_array[atom_number2] = spin2_initial[0];
atoms::y_spin_array[atom_number2] = spin2_initial[1];
atoms::z_spin_array[atom_number2] = spin2_initial[2];
cmc::energy_reject += 1.0;
}
//}
}
// if s2 not on unit sphere
else{
atoms::x_spin_array[atom_number1] = spin1_initial[0];
atoms::y_spin_array[atom_number1] = spin1_initial[1];
atoms::z_spin_array[atom_number1] = spin1_initial[2];
cmc::sphere_reject+=1.0;
}
} // end of cmc move
cmc::mc_total += 1.0;
} // end of mc loop
return EXIT_SUCCESS;
}
///
/// @brief Runs the Constrained Monte Carlo algorithm
///
/// Chooses nspins random spin pairs from the spin system and attempts a
/// Constrained Monte Carlo move on each pair, accepting for either lower
/// energy or with a Boltzmann thermal weighting.
///
/// @return void
///
int ConstrainedMonteCarlo(){
// Check for calling of function
if(err::check==true) std::cout << "sim::ConstrainedMonteCarlo has been called" << std::endl;
// check for cmc initialisation
if(cmc::is_initialised==false) CMCinit();
int atom_number1;
int atom_number2;
int imat1;
int imat2;
double delta_energy1;
double delta_energy2;
double delta_energy21;
double Eold;
double Enew;
std::valarray<double> spin1_initial(3);
std::valarray<double> spin1_final(3);
double spin2_initial[3];
double spin2_final[3];
double spin1_init_mvd[3];
double spin1_fin_mvd[3];
double spin2_init_mvd[3];
double spin2_fin_mvd[3];
double M_other[3];
double Mz_old;
double Mz_new;
double probability;
// Material dependent temperature rescaling
std::vector<double> rescaled_material_kBTBohr(mp::num_materials);
std::vector<double> sigma_array(mp::num_materials); // range for tuned gaussian random move
for(int m=0; m<mp::num_materials; ++m){
double alpha = mp::material[m].temperature_rescaling_alpha;
double Tc = mp::material[m].temperature_rescaling_Tc;
double rescaled_temperature = sim::temperature < Tc ? Tc*pow(sim::temperature/Tc,alpha) : sim::temperature;
rescaled_material_kBTBohr[m] = 9.27400915e-24/(rescaled_temperature*1.3806503e-23);
sigma_array[m] = rescaled_temperature < 1.0 ? 0.02 : pow(1.0/rescaled_material_kBTBohr[m],0.2)*0.08;
}
// copy matrices for speed
double ppolar_vector[3];
double ppolar_matrix[3][3];
double ppolar_matrix_tp[3][3];
for (int i=0;i<3;i++){
ppolar_vector[i]=cmc::polar_vector[0][i];
for (int j=0;j<3;j++){
ppolar_matrix[i][j]=cmc::polar_matrix[i][j];
ppolar_matrix_tp[i][j]=cmc::polar_matrix_tp[i][j];
}
}
//sigma = ((kbT_bohr)**0.2)*0.08_dp
//inv_kbT_bohr = 1.0_dp/kbT_bohr
M_other[0] = 0.0;
M_other[1] = 0.0;
M_other[2] = 0.0;
for(int atom=0;atom<atoms::num_atoms;atom++){
const double mu = atoms::m_spin_array[atom];
M_other[0] = M_other[0] + atoms::x_spin_array[atom] * mu; //multiplied by polar_vector below
M_other[1] = M_other[1] + atoms::y_spin_array[atom] * mu;
M_other[2] = M_other[2] + atoms::z_spin_array[atom] * mu;
}
for (int mcs=0;mcs<atoms::num_atoms;mcs++){
// Randomly select spin number 1
atom_number1 = int(mtrandom::grnd()*atoms::num_atoms);
imat1=atoms::type_array[atom_number1];
// get spin moment for atom 1
const double mu1 = atoms::m_spin_array[atom_number1];
sim::mc_delta_angle=sigma_array[imat1];
// Save initial Spin 1
spin1_initial[0] = atoms::x_spin_array[atom_number1];
spin1_initial[1] = atoms::y_spin_array[atom_number1];
spin1_initial[2] = atoms::z_spin_array[atom_number1];
//spin1_init_mvd = matmul(polar_matrix, spin1_initial)
spin1_init_mvd[0]=ppolar_matrix[0][0]*spin1_initial[0]+ppolar_matrix[0][1]*spin1_initial[1]+ppolar_matrix[0][2]*spin1_initial[2];
spin1_init_mvd[1]=ppolar_matrix[1][0]*spin1_initial[0]+ppolar_matrix[1][1]*spin1_initial[1]+ppolar_matrix[1][2]*spin1_initial[2];
spin1_init_mvd[2]=ppolar_matrix[2][0]*spin1_initial[0]+ppolar_matrix[2][1]*spin1_initial[1]+ppolar_matrix[2][2]*spin1_initial[2];
// Make Monte Carlo move
sim::mc_move(spin1_initial,spin1_final);
//spin1_fin_mvd = matmul(polar_matrix, spin1_final)
spin1_fin_mvd[0]=ppolar_matrix[0][0]*spin1_final[0]+ppolar_matrix[0][1]*spin1_final[1]+ppolar_matrix[0][2]*spin1_final[2];
spin1_fin_mvd[1]=ppolar_matrix[1][0]*spin1_final[0]+ppolar_matrix[1][1]*spin1_final[1]+ppolar_matrix[1][2]*spin1_final[2];
spin1_fin_mvd[2]=ppolar_matrix[2][0]*spin1_final[0]+ppolar_matrix[2][1]*spin1_final[1]+ppolar_matrix[2][2]*spin1_final[2];
// Calculate Energy Difference 1
//call calc_one_spin_energy(delta_energy1,spin1_final,atom_number1)
// Calculate current energy
Eold = sim::calculate_spin_energy(atom_number1);
// Copy new spin position (provisionally accept move)
atoms::x_spin_array[atom_number1] = spin1_final[0];
atoms::y_spin_array[atom_number1] = spin1_final[1];
atoms::z_spin_array[atom_number1] = spin1_final[2];
// Calculate new energy
Enew = sim::calculate_spin_energy(atom_number1);
// Calculate difference in Joules/mu_B
delta_energy1 = (Enew-Eold)*mp::material[imat1].mu_s_SI*1.07828231e23; //1/9.27400915e-24
// Compute second move
// Randomly select spin number 2 (i/=j)
atom_number2 = int(mtrandom::grnd()*atoms::num_atoms);
imat2=atoms::type_array[atom_number2];
// get spin moment for atom 2
const double mu2 = atoms::m_spin_array[atom_number2];
// Save initial Spin 2
spin2_initial[0] = atoms::x_spin_array[atom_number2];
spin2_initial[1] = atoms::y_spin_array[atom_number2];
spin2_initial[2] = atoms::z_spin_array[atom_number2];
//spin2_init_mvd = matmul(polar_matrix, spin2_initial)
spin2_init_mvd[0]=ppolar_matrix[0][0]*spin2_initial[0]+ppolar_matrix[0][1]*spin2_initial[1]+ppolar_matrix[0][2]*spin2_initial[2];
spin2_init_mvd[1]=ppolar_matrix[1][0]*spin2_initial[0]+ppolar_matrix[1][1]*spin2_initial[1]+ppolar_matrix[1][2]*spin2_initial[2];
spin2_init_mvd[2]=ppolar_matrix[2][0]*spin2_initial[0]+ppolar_matrix[2][1]*spin2_initial[1]+ppolar_matrix[2][2]*spin2_initial[2];
// Calculate new spin based on constraint Mx=My=0
const double mom_ratio = (mu1/mu2);
spin2_fin_mvd[0] = mom_ratio*(spin1_init_mvd[0]-spin1_fin_mvd[0]) + spin2_init_mvd[0];
spin2_fin_mvd[1] = mom_ratio*(spin1_init_mvd[1]-spin1_fin_mvd[1]) + spin2_init_mvd[1];
if(((spin2_fin_mvd[0]*spin2_fin_mvd[0]+spin2_fin_mvd[1]*spin2_fin_mvd[1])<1.0) && (atom_number1 != atom_number2)){
spin2_fin_mvd[2] = vmath::sign(spin2_init_mvd[2])*sqrt(1.0-spin2_fin_mvd[0]*spin2_fin_mvd[0] - spin2_fin_mvd[1]*spin2_fin_mvd[1]);
//spin2_final = matmul(polar_matrix_tp, spin2_fin_mvd)
spin2_final[0]=ppolar_matrix_tp[0][0]*spin2_fin_mvd[0]+ppolar_matrix_tp[0][1]*spin2_fin_mvd[1]+ppolar_matrix_tp[0][2]*spin2_fin_mvd[2];
spin2_final[1]=ppolar_matrix_tp[1][0]*spin2_fin_mvd[0]+ppolar_matrix_tp[1][1]*spin2_fin_mvd[1]+ppolar_matrix_tp[1][2]*spin2_fin_mvd[2];
spin2_final[2]=ppolar_matrix_tp[2][0]*spin2_fin_mvd[0]+ppolar_matrix_tp[2][1]*spin2_fin_mvd[1]+ppolar_matrix_tp[2][2]*spin2_fin_mvd[2];
// Automatically accept move for Spin1 - now before if ^^
//atomic_spin_array(:,atom_number1) = spin1_final(:)
//Calculate Energy Difference 2
// Calculate current energy
Eold = sim::calculate_spin_energy(atom_number2);
// Copy new spin position (provisionally accept move)
atoms::x_spin_array[atom_number2] = spin2_final[0];
atoms::y_spin_array[atom_number2] = spin2_final[1];
atoms::z_spin_array[atom_number2] = spin2_final[2];
// Calculate new energy
Enew = sim::calculate_spin_energy(atom_number2);
// Calculate difference in Joules/mu_B
delta_energy2 = (Enew-Eold)*mp::material[imat2].mu_s_SI*1.07828231e23; //1/9.27400915e-24
// Calculate Delta E for both spins
delta_energy21 = delta_energy1*rescaled_material_kBTBohr[imat1] + delta_energy2*rescaled_material_kBTBohr[imat2];
// Compute Mz_other, Mz, Mz'
Mz_old = M_other[0]*ppolar_vector[0] + M_other[1]*ppolar_vector[1] + M_other[2]*ppolar_vector[2];
Mz_new = (M_other[0] + mu1*spin1_final[0] + mu2*spin2_final[0]- mu1*spin1_initial[0] - mu2*spin2_initial[0])*ppolar_vector[0] +
(M_other[1] + mu1*spin1_final[1] + mu2*spin2_final[1]- mu1*spin1_initial[1] - mu2*spin2_initial[1])*ppolar_vector[1] +
(M_other[2] + mu1*spin1_final[2] + mu2*spin2_final[2]- mu1*spin1_initial[2] - mu2*spin2_initial[2])*ppolar_vector[2];
// Check for lower energy state and accept unconditionally
//if((delta_energy21<0.0) && (Mz_new>0.0)) continue;
// Otherwise evaluate probability for move
//else{
// If move is favorable then accept
probability = exp(-delta_energy21)*((Mz_new/Mz_old)*(Mz_new/Mz_old))*std::fabs(spin2_init_mvd[2]/spin2_fin_mvd[2]);
if((probability>=mtrandom::grnd()) && (Mz_new>0.0) ){
M_other[0] = M_other[0] + mu1*spin1_final[0] + mu2*spin2_final[0] - mu1*spin1_initial[0] - mu2*spin2_initial[0];
M_other[1] = M_other[1] + mu1*spin1_final[1] + mu2*spin2_final[1] - mu1*spin1_initial[1] - mu2*spin2_initial[1];
M_other[2] = M_other[2] + mu1*spin1_final[2] + mu2*spin2_final[2] - mu1*spin1_initial[2] - mu2*spin2_initial[2];
cmc::mc_success += 1.0;
}
//if both p1 and p2 not allowed then
else{
// reset spin positions
atoms::x_spin_array[atom_number1] = spin1_initial[0];
atoms::y_spin_array[atom_number1] = spin1_initial[1];
atoms::z_spin_array[atom_number1] = spin1_initial[2];
atoms::x_spin_array[atom_number2] = spin2_initial[0];
atoms::y_spin_array[atom_number2] = spin2_initial[1];
atoms::z_spin_array[atom_number2] = spin2_initial[2];
cmc::energy_reject += 1.0;
}
//}
}
// if s2 not on unit sphere
else{
atoms::x_spin_array[atom_number1] = spin1_initial[0];
atoms::y_spin_array[atom_number1] = spin1_initial[1];
atoms::z_spin_array[atom_number1] = spin1_initial[2];
cmc::sphere_reject+=1.0;
}
cmc::mc_total += 1.0;
}
return EXIT_SUCCESS;
}