The Change in Energy upon a Proposed Spin Flip

dE() is function that accepts as arguments the 2D array of spins, M; the side-length, L, and a position $(i,j)$, and returns the change in energy (in units of $J$) upon flipping spin $(i,j)$, without actually flipping it. All variables are of integer type, int. The syntax ** M means that M is a pointer to a pointer to an int, signifying that M is a 2D array. To access element in row i and column j in M, the syntax is M[i][j]. In C, all array indices start at 0, so M[0][0] refers to the “upper-left” corner of the magnet (assuming row numbers increase going down the magnet). The inline conditional syntax i?(i-1):(L-1) expands as, “If i is non-zero, return i-1; otherwise, return L-1.” This implements periodic boundaries when looking to the west of spin M[i][j]. The syntax (i+1)\%L returns computes $(i+1)\mod L$, which also implements periodic boundaries when looking to the east of spin M[i][j].

int dE ( int ** M, int L, int i, int j ) {
  return -2*(M[i][j])*(M[i?(i-1):(L-1)][j]+M[(i+1)%L][j]+
		      M[i][j?(j-1):(L-1)]+M[i][(j+1)%L]);
}