Chaos, broken hyperscaling, and nonuniversality in a spin glass

Recently extended precise numerical methods and newly modified scaling arguments allow for a coherent picture of the glassy state in a two-dimensional spin glass to be assembled. This glassy state, where the correlation length is larger than the system size, is characterized by ``chaos,'' the extreme sensitivity of the state to temperature. This chaos is shown to lead to a breakdown of hyperscaling in spin glasses. The length scale at which entropy becomes important is found to depend on the type of randomness, so that though there is a type of universality, the critical exponents depend on the distribution of disorder. The numerical simulations use multiprecision arithmetic to exactly compute the partition function in samples of sizes up to $L^2=512^2$ down to temperatures of less than $J/20$, where the typical strength of the disorder is $J$. These results can be used in support of studies of the non-equilibrium behavior of glassy models.