Ising 1-Dimensional C - program - c

Question

i am trying to simulate the Ising Model 1-D. This model consists in a chain of spin (100 spins) and using the Mont Carlo - Metropolis to accept the flip of a spin if the energy of the system (unitary) goes down or if it will be less than a random number.
In the correct program, both the energy the magnetization go to zero, and we have the results as a Gaussian (graphics of Energyor the magnetization by the number of Monte Carlo steps).
I have done some work but i think my random generator isn't correctt for this, and i don't know how/where to implement the boundary conditions: the last spin of the chain is the first one.
I need help to finish it. Any help will be welcome. Thank you.
I am pasting my C program down:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h> //necessary for function time()
#define LENGTH 100 //size of the chain of spins
#define TEMP 2 // Temperature in units of J
#define WARM 200 // Termalização
#define MCS 20000 //Monte Carlo Steps
void start( int spin[])
{
/* starts with all the spins 1 */
int i;
for (i = 0 ; i < 100; i++)
{
spin[i] = 1;
}
}
double energy( int spin[]) //of the change function J=1
{
int i;
double energyX=0;// because the begining Energy = -J*sum (until 100) =-100,
for (i = 0;i<100;i++)
energyX=energyX-spin[i]*spin[i+1];
return(energyX);
}
int randnum(){
int num;
srand(time(NULL));
/* srand(time(NULL)) objectives to initiate the random number generator
with the value of the function time(NULL). This is calculated as being the
total of seconds passed since january first of 1970 until the present date.
So, this way, for each execution the value of the "seed" will be different.
*/
srand(time(NULL));
//picking one spin randomly zero to 100
num=rand() % 100;
printf("num = %d ", num);
return num;
}
void montcarlo( int spin[])
{
int i,j,num;
double prob;
double energyA, energyB; // A -> old energy and B -> the new energy
int rnum1,rnum2;
prob=exp(-(energyB-energyA)/TEMP);
energyA = 0;
energyB = 0;
for (i = 0;i<100;i++)
{
for (j = 0;j<100;j++)
{
energyA=energy(spin);
rnum1=randnum();
rnum2=randnum(); // i think they will give me different numbers
spin[rnum1] = -spin[rnum1]; //flip of the randomly selected spin
energyB = energyB-spin[j]*spin[j+1];
if ((energyB-energyA<0)||((energyB-energyA>0)&&(rnum2>prob))){ // using rnum2 not to be correlated if i used rnum1
spin[rnum1]=spin[rnum1];} // keep the flip
else if((energyB-energyA>0)&&(rnum2<prob))
spin[rnum1]=-spin[rnum1]; // unflip
}
}
}
int Mag_Moment( int spin[] ) // isso é momento magnetico
{
int i;
int mag;
for (i = 0 ; i < 100; i++)
{
mag = mag + spin[i];
}
return(mag);
}
int main()
{
// starting the spin's chain
int spin[100];//the vector goes til LENGHT=100
int i,num,j;
int itime;
double mag_moment;
start(spin);
double energy_chain=0;
energy_chain=energy(spin); // that will give me -100 in the begining
printf("energy_chain starts with %f", energy_chain);// initially it gives -100
/*Warming it makes the spins not so ordered*/
for (i = 1 ; i <= WARM; i++)
{
itime = i;
montcarlo(spin);
}
printf("Configurtion after warming %d \n", itime);
for (j = 0 ; j < LENGTH; j++)
{
printf("%d",spin[j]);
}
printf("\n");
energy_chain=energy(spin); // new energy after the warming
/*openning a file to save the values of energy and magnet moment of the chain*/
FILE *fp; // declaring the file for the energy
FILE *fp2;// declaring the file for the mag moment
fp=fopen("energy_chain.txt","w");
fp2=fopen("mag_moment.txt","w");
int pures;// net value of i
int a;
/* using Monte Carlo metropolis for the whole chain */
for (i = (WARM + 1) ; i <= MCS; i++)
{
itime=i;//saving the i step for the final printf.
pures = i-(WARM+1);
montcarlo(spin);
energy_chain = energy_chain + energy(spin);// the spin chain is moodified by void montcarlo
mag_moment = mag_moment + Mag_Moment(spin);
a=pures%10000;// here i select a value to save in a txt file for 10000 steps to produce graphs
if (a==0){
fprintf(fp,"%.12f\n",energy_chain); // %.12f just to give a great precision
fprintf(fp2,"%.12f\n",mag_moment);
}
}
fclose(fp); // closing the files
fclose(fp2);
/* Finishing -- Printing */
printf("energy_chain = %.12f\n", energy_chain);
printf("mag_moment = %.12f \n", mag_moment);
printf("Temperature = %d,\n Size of the system = 100 \n", TEMP);
printf("Warm steps = %d, Montcarlo steps = %d \n", WARM , MCS);
printf("Configuration in time %d \n", itime);
for (j = 0 ; j < 100; j++)
{
printf("%d",spin[j]);
}
printf("\n");
return 0;
}

Answer 1

you should call srand(time(NULL)); only once in your program. Every time you call this in the same second you will get the same sequence of random numbers. So it is very likely that both calls to randnum will give you the same number.
Just add srand(time(NULL)); at the begin of main and remove it elsewhere.

Answer 2

I see a number of bugs in this code, I think. The first one is the re-seeding of the srand() each loop which has already been addressed. Many of the loops go beyond the array bounds, such as:
for (ii = 0;ii<100;ii++)
{
energyX = energyX - spin[ii]*spin[ii+1];
}
This will give you spin[99]*spin[100] for the last loop, for which is out of bounds. That is kind of peppered throughout the code. Also, I noticed the probability rnum2 is an int but compared as if it's supposed to be a double. I think dividing the rnum2 by 100 will give a reasonable probability.
rnum2 = (randnum()/100.0); // i think they will give me different numbers
The initial probability used to calculate the spin is, prob=exp(-(energyB-energyA)/TEMP); but both energy values are not initialized, maybe this is intentional, but I think it would be better to just use rand(). The Mag_Moment() function never initializes the return value, so you wind up with a return value that is garbage. Can you point me to the algorithm you are trying to reproduce? I'm just curious.