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Flipping state: Metropolis in Ising model

  1. Apr 8, 2014 #1
    1. The problem statement, all variables and given/known data

    Hi everyone, I'm having some difficulties with my code:

    1. Randomly Choose a lattice at position (x, y) within the NxN lattice
    2. Why by writing "int x = int(drand48()*L);" and "int y = int(drand48()*L);" it doesn't extract the value stored at that location (x, y)?
    3. Calculate change in energy (dE) if flipped
    4. If dE < 0, flip. If dE> 0, flip only with acceptance rate given by boltzmann exponential (which is between 0 and 1).


    I'm referring to some possible codes already written online:

    http://physics.clarku.edu/sip/programs/C/chapter17/ising.h
    http://www.pages.drexel.edu/~cfa22/msim/node11.html

    I'm still learning to code in C++, so there are many things I don't really get, so please bear with me.

    2. Relevant equations

    Here's the general structure of my code so far:

    1. Generating a matrix
    2. Assigning randomly +/- 1 to each site
    3. Choosing a site randomly
    4. If dE < 0, flip. If dE > 0, then flip only with acceptance rate given by boltzmann exponential.


    3. The attempt at a solution

    Code (Text):


    #include <cstdlib>
    #include <ctime>
    using namespace std;
    #include <iostream>
    int main() //random generation of spin configuration
    {
    int L;              //Total number of spins L = NxN
    double B=1;         //magnetic field
    double M;           //Total Magnetization = Sum Si
    double E;           //Total Energy
    int T = 1.0;
    int nsweeps = 100;      //number of sweeps
    int de;             //change in energy when flipped
    double Boltzmann;       //Boltzmann factor
    int x,y;            //randomly chosen lattice site
    int i,j,a,c;            //counters
      int ROWS = 5;
      int COLS = 5;
      int matrix[ROWS][COLS];
      srand ( static_cast<unsigned> ( time ( 0 ) ) );
      for ( int i = 0; i < ROWS; i++ )
      {
        for ( int j = 0; j < COLS; j++ )
        {
          matrix[i][j] = rand () % 2 *2-1;
        }
      }

     // showing the matrix on the screen
        for(int i=0;i<ROWS;i++)  // loop 3 times for three lines
        {
            for(int j=0;j<COLS;j++)  // loop for the three elements on the line
            {
                cout<<matrix[i][j];  // display the current element out of the array
            }
        cout<<endl;  // when the inner loop is done, go to a new line
        }
        return 0;  // return 0 to the OS.

    //boundary conditions and range
    if(x<0) x += N;      
    if(x>=L) x -= N;
    if(y<0) y += N;
    if(y>=L) y -= N;

    //counting total energy of configuration
    {  int neighbour = 0;    // nearest neighbour count

       for(int i=0; i<L; i++)
          for(int j=0; j<L; j++)
        {  if(spin(i,j)==spin(i+1, j))     // count from each spin to the right and above
                  neighbour++;
               else
                  neighbour--;
               if(spin(i, j)==spin(i, j+1))
                  neighbour++;
               else
                  neighbour--;
        }
       
        E = -J*neighbour - B*M;

    //flipping spin
    int x = int(drand48()*L);   //retrieves spin from randomly choosen site
    int y = int(drand48()*L);

    int delta_M = -2*(x, y);    //calculate change in Magnetization M
    int delta_neighbour = (x-1, y) + spin(x+1, y)+ spin(x, y-1) + spin(x, y+1);
    int delta_neighbour = -2*(x,y)* int delta_neighbour;

    double delta_E = -J*delta_neighbour -B*delta_M;


    //flip or not
    if (delta_E<=0)
        {  (x, y) *= -1;     // flip spin and update values
               M += delta_M;
               E += delta_E;
           
            }

       

    }

     
     
  2. jcsd
  3. Apr 9, 2014 #2
  4. Apr 9, 2014 #3

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Your code doesn't even compile. The braces don't match. What's N? What's J? What's spin?
    What's this: int delta_neighbour = -2*(x,y)* int delta_neighbour; ?
     
  5. Apr 10, 2014 #4
    Ok, I've realised my code is too messy so I've decided to break the code into portions, each portion doing one thing. Let's start with these two portions:

    1. Generate NxN lattice with -1 or +1 at each site randomly.
    2. How to extract the value at a site at location (x, y).

    Part 1 of code:

    Code (Text):

    //Generate NxN lattice with -1 or +1 at each site randomly.

    #include <stdlib.h>
    #include <iostream>
    #include <cstdlib>
    #include <ctime>
    using namespace std;

    #define spin(a, b) (matrix[(a)][(b)])  //function spin (a, b) extracts value of site at location (a, b)

    int main()
    {

    const int LatSize = 5;
    const int L = LatSize * LatSize;
    int matrix[LatSize][LatSize];


    srand ( static_cast<unsigned> ( time ( 0 ) ) );
    for ( int i = 0; i < LatSize; i++ )
    {
    for ( int j = 0; j < LatSize; j++ )
    {
    matrix[i][j] = rand () % 2 *2-1;
    }
    }

    //End of Generating matrix
     
    Part 2 of code:
    Code (Text):

    //Extracting value of a site at location (x,y)


    int x = int (rand()*LatSize);
    int y = int (rand()*LatSize);

    int delta_M = -2*spin(x, y); //change in magnetization energy

    int delta_neighbour = spin(x-1, y) + spin(x+1, y)+ spin(x, y-1) + spin(x, y+1);
    delta_neighbour = -2*spin(x,y)* delta_neighbour; //change in neighbour product energy

    cout << delta_neighbour;

    //End of extracting value of site at (x, y)

    return 0;
    }
     
    Doesn't seem to work, as it doesn't display the value of delta_neighbour..
     
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