dft_tools/doc/reference/c++/statistics/ising2d_0.cpp

#include <triqs/mc_tools/random_generator.hpp>
#include <triqs/mc_tools/mc_generic.hpp>
#include <triqs/utility/callbacks.hpp>
#include <triqs/arrays.hpp>
#include <triqs/statistics.hpp>
#include <vector>
#include <iostream>
#include <fstream>
//#define TRIQS_ARRAYS_ENFORCE_BOUNDCHECK
// H = -J \sum_<ij> s_i s_j - h \sum_i s_i 
// theoretical T_c = 2/log(1+sqrt(2)) for J = 1.0
using namespace triqs::statistics;
/**************
 * config 
 **************/

struct configuration {
 // N is the linear size of spin matrix, M the total magnetization,
 // beta the inverse temperature, J the coupling,
 // field the magnetic field and energy the energy of the configuration
 int N, M;
 double beta, J, field, energy;
 // the chain of spins: true means "up", false means "down"
 triqs::arrays::array<bool,2> chain;
 observable<double> M_stack;

 // constructor
 configuration(int N_, double beta_, double J_, double field_):
  N(N_), M(-N*N), beta(beta_), J(J_), field(field_), energy(-J*4*N/2+N*field), chain(N,N) , M_stack(){
   chain()=false;
  }

};

/**************
 * move
 **************/

// A move flipping a random spin
struct flip {
 configuration * config;
 triqs::mc_tools::random_generator &RNG;

 struct site { int i,j ;};//small struct storing indices of a given site
 site s;
 double delta_energy;

 // constructor
 flip(configuration & config_, triqs::mc_tools::random_generator & RNG_) :
  config(&config_), RNG(RNG_) {}

 // find the neighbours with periodicity
 std::vector<site> neighbors(site s, int N){
  std::vector<site> nns(4);
  int counter=0;
  for(int i=-1;i<=1;i++){
   for(int j=-1;j<=1;j++){
    if ((i==0) != (j==0)) //xor
     nns[counter++] = site{(s.i+i)%N, (s.j+j)%N};
   }
  }
  return nns;
 }
 double attempt() {
  // pick a random site
  int index = RNG(config->N*config->N);
  s = {index%config->N, index/config->N};

  // compute energy difference from field
  delta_energy = (config->chain(s.i,s.j) ? 2 : -2) * config->field;
  auto nns = neighbors(s,config->N); //nearest-neighbors
  double sum_neighbors=0.0;
  for(auto & x:nns) sum_neighbors += ((config->chain(x.i,x.j))?1:-1);
  // compute energy difference from J
  delta_energy += - sum_neighbors * config->J* (config->chain(s.i,s.j)?-2:2);

  // return Metroplis ratio
  return std::exp(-config->beta * delta_energy);
 }

 // if move accepted just flip site and update energy and magnetization
 double accept() {
  config->M += (config->chain(s.i,s.j) ? -2 : 2);
  config->chain(s.i,s.j) = !config->chain(s.i,s.j);
  config->energy += delta_energy;
  return 1.0;
 }

 // nothing to do if the move is rejected
 void reject() {}
};


/**************
 * measure
 **************/
struct compute_m {

 configuration * config;
 double Z, M;

 compute_m(configuration & config_) : config(&config_), Z(0), M(0) {}

 // accumulate Z and magnetization
 void accumulate(int sign) {

  Z += sign;
  M += config->M;
  //config->M_stack << double(config->M/(config->N*config->N));
  config->M_stack << config->M;
 }

 // get final answer M / (Z*N)
 void collect_results(boost::mpi::communicator const &c) {

  double sum_Z, sum_M;
  boost::mpi::reduce(c, Z, sum_Z, std::plus<double>(), 0);
  boost::mpi::reduce(c, M, sum_M, std::plus<double>(), 0);

  if (c.rank() == 0) {
   std::cout << "@Beta:\t"<<config->beta<<"\tMagnetization:\t" << sum_M / (sum_Z*(config->N*config->N)) << std::endl ;
   std::cout << "average_and_error(M) = " << average_and_error(config->M_stack) << std::endl;
   std::cout << "#Beta:\t"<<config->beta<<"\tAutocorr_time:\t" << autocorrelation_time_from_binning(config->M_stack) << std::endl; 
   std::ofstream outfile("magnetization_series.dat");
   for(int i=0;i<config->M_stack.size();i++)
    outfile << config->M_stack[i] <<std::endl;
   outfile.close();
  }

 }
};

int main(int argc, char* argv[]) {

 // initialize mpi
 boost::mpi::environment env(argc, argv);
 boost::mpi::communicator world;

 double H=0.0,B=0.5;
 int N=20;
 int nc = 100000;
 if(argc==4){
  H = atof(argv[1]);//field
  B = atof(argv[2]);//inverse temp
  N = atoi(argv[3]);//size along one dimension
  nc = 1000000 ;
 }
 if (world.rank() == 0) 
  std::cout << "2D Ising with field = " << H << ", beta = " << B << ", N = " << N << std::endl;

 // Prepare the MC parameters
 int n_cycles = nc;
 int length_cycle = 100;
 int n_warmup_cycles = 100000;
 std::string random_name = "";
 int random_seed = 374982 + world.rank() * 273894;
 int verbosity = (world.rank() == 0 ? 2 : 0);

 // Construct a Monte Carlo loop
 triqs::mc_tools::mc_generic<double> IsingMC(n_cycles, length_cycle, n_warmup_cycles,
   random_name, random_seed, verbosity);

 // parameters of the model
 int length = N;
 double J = 1.0;
 double field = H;
 double beta = B;

 // construct configuration
 configuration config(length, beta, J, field);

 // add moves and measures
 IsingMC.add_move(flip(config, IsingMC.rng()), "spin flip");
 IsingMC.add_measure(compute_m(config), "measure magnetization");

 // Run and collect results
 IsingMC.start(1.0, triqs::utility::clock_callback(-1));
 IsingMC.collect_results(world);

 return 0;
}