CORRELATION LENGTH OF THE TWO-DIMENSIONAL RANDOM FIELD ISING MODEL VIA GREEDY LATTICE ANIMAL

For the two-dimensional random field Ising model where the random field is given by independent and identically distributed mean zero Gaussian variables with variance 2, we study (one natural notion of) the correlation length, which is the critical size of a box at which the influences of the random field and of the boundary condition on the spin magnetization are comparable. We show that as 0, at zero temperature the correlation length scales as e,.⠂4=3/ (and our upper bound applies for all positive temperatures).

Automated summary

In this paper, we investigate the two-dimensional random field Ising model with mean zero Gaussian variables and variance 2. We analyze the correlation length, which represents the critical box size where the random field and boundary condition have comparable effects on spin magnetization. Our results show that the correlation length scales exponentially as e,⠂4=3/ as 0, and our upper bound is applicable for all positive temperatures.