Low temperature behavior of the twodimensional Ising spin glass
Abstract
We study the twodimensional Ising spin glass with a Gaussian distribution of bonds, using an efficient parallel tempering cluster Monte Carlo algorithm due to Houdayer.We perform a finitesize scaling analysis of data for the correlation length of the system, ξ_L. In the finitesize region at low T where ξ_{L} ≫ L (the lattice has N=L^2 sites), scaling works well with the expected value of the stiffness exponent, θ ≃ 0.29, obtained from many zerotemperature studies. However, in the ``bulk'' region at higher T where ξ_{L} ≪ L, the effective value of the critical exponent ν describing the divergence of the bulk correlation length at T=0, does not quite reach its expected value of 1/θ even for the largest size studied, L=128. Nonetheless, the exponent does seem to approach 1/θ as L increases. This observation, that very large sizes are needed to see asymptotic bulk behavior at finite temperature, explains why earlier simulations, which were for smaller sizes, found ν to be significantly smaller than 1/θ.
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MARL25012L