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cdw_pam.cpp
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cdw_pam.cpp
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#include <iostream>
#include <fstream>
#include <cmath>
#include <string>
#include <vector>
#define PI acos(-1.0)
using namespace std;
struct Parameters
{
double g, K, V, t;
Parameters(double g, double K, double V, double t)
{
this->g = g;
this->K = K;
this->V = V;
this->t = t;
}
};
double square(double a)
{
return a*a;
}
double epsilon(double kx, double ky, double t)
{
return -2*t*(cos(kx) + cos(ky));
}
double energy(double kx, double ky, double t, double Delta)
{
return sqrt(square(epsilon(kx,ky,t)) + square(Delta));
}
double summand(double Ek, double V, double beta)
{
double one, two;
one = 1.0/Ek*(1.0 - Ek/sqrt(square(Ek) + 4*square(V)))*tanh(0.25*beta*(Ek - sqrt(square(Ek) + 4*square(V))));
two = 1.0/Ek*(1.0 + Ek/sqrt(square(Ek) + 4*square(V)))*tanh(0.25*beta*(Ek + sqrt(square(Ek) + 4*square(V))));
return one + two;
}
double f(const Parameters &p, double beta, double Delta)
{
double g, K, V, t;
g = p.g;
K = p.K;
V = p.V;
t = p.t;
double s = 0;
int Nx = 100;
int Ny = 100;
double Ek;
double kx, ky;
double increment;
for (int nx = -Nx/2; nx <= Nx/2; ++nx)
{
for (int ny = -Ny/2; ny <= Ny/2; ++ny)
{
kx = 2*nx*PI/Nx;
ky = 2*ny*PI/Ny;
Ek = energy(kx, ky, t, Delta);
s = s + summand(Ek, V, beta);
}
}
s = s*2*square(g)/(K*Nx*Ny);
s = s - 1.0;
return s;
}
double fprime(const Parameters &p, double beta, double Delta)
{
double dDelta = 0.00001;
return (f(p,beta,Delta+dDelta) - f(p,beta,Delta))/dDelta;
}
double newton(double (*f)(const Parameters &p, double beta, double Delta), const Parameters &p, double beta)
{
double x0 = 3.0;
double x1 = x0 - f(p, beta, x0)/fprime(p,beta,x0);
int count = 0;
int iterationMax = 8;
while(fabs(x0 - x1) > 0.001)
{
count = count + 1;
x0 = x1;
x1 = x0 - f(p,beta,x0)/fprime(p,beta,x0);
if (count > iterationMax)
{
cout << "No solution found. " << endl;
break;
//exit(-1);
}
}
return x1;
}
int main(int argc, char **argv)
{
double g, K, V, t;
double beta;
double Delta;
double increment;
g = 1.0;
K = 1.0;
V = 0;
t = 1.0;
Parameters p(g,K,V,t);
if (false)
{
increment = 0.1;
beta = 1000.0;
ofstream ofile;
ofile.open("f.txt");
for (int i = 0; i < 100; ++i)
{
Delta = increment*(i+0.5);
ofile << Delta << " " << f(p, beta, Delta) << endl;
}
ofile.close();
return 0;
}
if (false)
{
double V0 = 0;
double V1 = 1.8269075;
int NV = 100;
double dV = (V1 - V0)/NV;
beta = 10000;
for (int i = 0; i <= NV; ++i)
{
V = V0 + i*dV;
Parameters parameters(g, K, V, t);
cout << V << " " << newton(f,parameters,beta) << endl;
}
return 0;
}
vector<double> T;
double T0;
double T1;
T0 = 1.88;
T1 = 1.8846;
int NT = 30;
double dT = (T1 - T0)/NT;
for (int i = 0; i <= NT; ++i)
{
T.push_back(T0+i*dT);
}
for (int i = 0; i < T.size(); ++i)
{
beta = 1.0/T[i];
cout << T[i] << " " << newton(f, p, beta) << endl;
}
return 0;
}