Equilibrium Statistical Mechanics

Citations refer to Papers (since 1989)

My past work on Equilibrium Statistical Mechanics (after 1988) included development of efficient simulation techniques for systems with slow dynamics [12] , [T3] . We studied critical slowing down in Ising and Potts ferromagnets in d=2 [1] , the fully frustrated Ising model [5] , [15] , [T3] , partially frustrated models and the Ashkin-Teller model with [23] , [25] and without [19] , [T5] disorder. The aim was to find efficient large-scale moves that allow a sluggish system to move fast ("jump") in configuration space, as opposed to the slow traditional methods that move one degree of freedom at a time.

Our studies of the Ashkin-Teller model with bond disorder [23] . led to the discovery [25] that various thermodynamic functions of this ferromagnetic system are non- self-averaging at criticality. We developed a finite size scaling theory [41] [42] for such random systems.

We discovered a very efficient way to perform non- parametric clustering of data, by using a physical system to provide a robust solution to this problem. [28] , [32] , [C4] , [C6] , [C8] , This work triggered my entry into my current field of interest - Bioinformatics; in particular - analysis of gene expression data.

My current interest in equilibrium Statistical Mechanics is limited to the problem of short - range spin glasses . By applying clustering methods to study short range spin glasses at T=0 [60] , [62] and at low T>0 [64] , [77] , we were able to interpret the hierarchical structure of state-space in terms of a hierarchy of correlated spin domains. We found that the low temperature phase of the short range spin glass is characteraized by a non-trivial overlap distribution P(q) , in agreeement with the results obtained for the model with infinite-range interactions. The structure of state space is, however, not ultrametric , as opposed to the infinite range model [77] . Currently we are extending this investigation to higher temperatures, and are studying the infinite-range model, looking for the "spin domains" that govern the hierarchical structure of it's low temperature phase.

Eytan Domany