It's always the little language-specific features that hang one up learning a new language.

Hello Fred,

just as a remark: Are you aware that you can simply wright:

isingarray = 2 RandomInteger[{0, 1}, {100, 100}] - 1;

Do [
temp = beta*(isingarray[[i + 1, j]] + isingarray[[i, j + 1]] + isingarray[[i - 1, j]] + isingarray[[i, j - 1]]);
z = E^temp + E^-temp; isingarray[[i, j]] = If[(E^-temp)/z > RandomReal[{0, 1}], 1, -1], {i, 2, 99}, 
{j, 2, 99}];

You do not need to use InitializationValue and the like - (nearly) nobody needs those functions, and they are qualified as "Experimental".

Regards -- Henrik

Hi Fred,

You need to Initialize the symbol to the persisted value before referencing it.

InitializationValue[isingarray] = 2 RandomInteger[{0, 1}, {100, 100}] - 1
Initialize[isingarray]