Equilibrium properties of disordered spin models with two scale interactions
Methods for understanding classical disordered spin systems with interact ions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Shorrington-Kirkpairick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdos-Renyi graph structures above the percolatiou threshold, and to Bathe lattices when appropriate boundary conditions apply. In this paper we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high temperature paramagnetic, spin glass and ferromagnetic phases by pert urbative schemes. We present results of a replica symmetric variational approximations where perturbative approaches fail at lower temperature. Results demonstrate novel reentrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high temperature transitions is found to be sensitive to the connectivity profile in the sparge sub-graph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.
Jack Raymond David Saad
Non-linearity and Complexity Research Group Anton University. Birmingham, UK
国际会议
International Workshop on Statistical Physics and Computer Sciences(统计物理与计算机科学交叉研究国际研讨会 )
北京
英文
178-205
2010-07-08（万方平台首次上网日期，不代表论文的发表时间）