I asked ChatGPT to produce some Ising model code for Project 3. Here is what I asked, but I'll only show the final outputs. -Please produce code in C for the 2D Ising model. -keep going -The two code fragments you produced were not complete. Could you please produce a complete code for the 2D Ising model. -I liked the style of the first version of the code. Could you complete the following code? [pasted code] -Could you please produce a Fortran 90 version of the code? -The Fortran version has at least one error arising because C is case sensitive and Fortran is not. Could you fix the Fortran version? -You're using j and J to represent two different variables, but in Fortran j and J are the same. -Why do you stop generating the reponse without completing the code? Please produce a full version -still there? [I had closed my laptop.] -Ok, let's try again. Please produce code in Fortran 90 for the 2D Ising model. Use a random seed based on the time. -Please don't stop generating code until the equilibration stage and the measuring stage are both finished. -and use the variabe Jexch for the exchange constant -keep going! -... (I tried a few other things but did not get much further.) Below are equivalent C and Fortran versions from ChatGPT for the 2D Ising model. Note that in the Fortran code, the exchange constant is J, which conflicts with integer variable j, and so should be renamed. #include #include #include #include #define N 32 // lattice size #define J 1.0 // exchange interaction strength #define kB 1.0 // Boltzmann constant #define warmupSteps 1000 // number of steps for equilibration #define measureSteps 100 // number of steps for measuring observables #define nTemps 100 // number of temperatures to simulate #define Tmin 1.0 // minimum temperature #define Tmax 5.0 // maximum temperature #define dT (Tmax-Tmin)/(nTemps-1) // temperature step size int main() { // Initialize the random number generator srand(time(NULL)); // Allocate memory for the spin lattice int **lattice; lattice = (int **)malloc(N * sizeof(int *)); for (int i = 0; i < N; i++) { lattice[i] = (int *)malloc(N * sizeof(int)); } // Initialize the spin lattice to a random configuration for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { if (rand() < RAND_MAX/2) { lattice[i][j] = 1; } else { lattice[i][j] = -1; } } } // Initialize the observables double energy = 0.0; double magnetization = 0.0; // Loop over temperatures for (int t = 0; t < nTemps; t++) { double T = Tmin + t*dT; printf("Temperature = %f\n", T); // Equilibration for (int i = 0; i < warmupSteps; i++) { // Choose a random spin int x = rand() % N; int y = rand() % N; // Compute the energy change if the spin is flipped int deltaE = 2*J*lattice[x][y]* (lattice[(x-1+N)%N][y] + lattice[(x+1)%N][y] + lattice[x][(y-1+N)%N] + lattice[x][(y+1)%N]); // Decide whether to flip the spin if (deltaE < 0 || exp(-deltaE/(kB*T)) > ((double)rand())/RAND_MAX) { lattice[x][y] = -lattice[x][y]; energy += deltaE; magnetization += 2*lattice[x][y]; } } // Measuring observables double sumEnergy = 0.0; double sumEnergy2 = 0.0; double sumMagnetization = 0.0; double sumMagnetization2 = 0.0; double sumAbsMagnetization = 0.0; for (int i = 0; i < measureSteps; i++) { // Choose a random spin int x = rand() % N; int y = rand() % N; // Compute the energy change if the spin is flipped int deltaE = 2*J*lattice[x][y]* (lattice[(x-1+N)%N][y] + lattice[(x+1)%N][y] + lattice[x][( program ising_2d implicit none integer, parameter :: N=32 ! lattice size real, parameter :: J=1.0 ! exchange interaction strength real, parameter :: kB=1.0 ! Boltzmann constant integer, parameter :: warmupSteps=1000 ! number of steps for equilibration integer, parameter :: measureSteps=100 ! number of steps for measuring observables integer, parameter :: nTemps=100 ! number of temperatures to simulate real, parameter :: Tmin=1.0 ! minimum temperature real, parameter :: Tmax=5.0 ! maximum temperature real, parameter :: dT=(Tmax-Tmin)/(nTemps-1) ! temperature step size integer :: i, j, t, x, y integer, dimension(N,N) :: lattice real :: T, energy, magnetization, deltaE real :: sumEnergy, sumEnergy2, sumMagnetization, sumMagnetization2, sumAbsMagnetization integer :: acceptCount ! Initialize the random number generator call srand(time()) ! Initialize the observables to zero energy = 0.0 magnetization = 0.0 ! Loop over temperatures do t=0, nTemps-1 T = Tmin + t*dT write(*,*) 'Temperature = ', T ! Equilibration do i=1, warmupSteps ! Choose a random spin x = mod(rand(), N) y = mod(rand(), N) ! Compute the energy change if the spin is flipped deltaE = 2.0*J*lattice(x,y)* & (lattice(mod(x-1+N,N),y) + & lattice(mod(x+1,N),y) + & lattice(x,mod(y-1+N,N)) + & lattice(x,mod(y+1,N))) ! Decide whether to flip the spin if (deltaE < 0.0 .or. exp(-deltaE/(kB*T)) > rand()/real(RAND_MAX)) then lattice(x,y) = -lattice(x,y) energy = energy + deltaE magnetization = magnetization + 2.0*lattice(x,y) endif end do ! Measuring observables sumEnergy = 0.0 sumEnergy2 = 0.0 sumMagnetization = 0.0 sumMagnetization2 = 0.0 sumAbsMagnetization = 0.0 acceptCount = 0 do i=1, measureSteps ! Choose a random spin x = mod(rand(), N) y = mod(rand(), N) ! Compute the energy change if the spin is flipped deltaE = 2.0*J*lattice(x,y)* & (lattice(mod(x-1+N,N),y) + & lattice(mod(x+1,N),y) + & lattice(x,mod(y-1+N,N)) + & lattice(x,mod(y+1,N))) ! Decide whether to flip the spin if (deltaE < 0.0 .or. exp(-deltaE/(kB*T)) > rand()/real(RAND_MAX)) then lattice(x,y) = -lattice(x,y) energy = energy + deltaE magnetization = magnetization + 2.0*lattice(x,y