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Journal of North University of China

Revision of Renormalization Group Solution for Spin Glass

XU Li-ping

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Spin glass model is discussed with real space renormalization group(RSRG) method,three kinds of fixed points and critical indices are deduced.Since a gap exists between the solution and the exact solution,revision is required.Some literatures indicate that it approaches exact solution if Kadanoff clusters are constructed with lager points,but the numeration increases greatly at the same time.Then a more efficient method is needed.The spin glass model is discussed with RSRG method by introducing an energy and temperature dependent weight factor.The new solution and the corresponding critical indices approach the exact solution more than those of before revision.

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Spin glass model is discussed with real space renormalization group(RSRG) method,three kinds of fixed points and critical indices are deduced.Since a gap exists between the solution and the exact solution,revision is required.Some literatures indicate that it approaches exact solution if Kadanoff clusters are constructed with lager points,but the numeration increases greatly at the same time.Then a more efficient method is needed.The spin glass model is discussed with RSRG method by introducing an energy and temperature dependent weight factor.The new solution and the corresponding critical indices approach the exact solution more than those of before revision.
By using real-space renormalization group (RG) methods, we show that spin glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two nonperturbative zero-temperature fixed points of the RG flow. We compute the critical exponents and discuss the RG flow and its relevance for three-dimensional systems. The new spin-glass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry-breaking theories. These results provide a new perspective on the long-standing debate about the behavior of spin glasses in a field.
Here is the first part of the summary of my work on random Ising model using real-space renormalization group (RSRG), also known as a Migdal-Kadanoff one. This approximate renormalization scheme was applied to the analysis thermodynamic properties of the model, and of probabilistic properties of a pair correlator, which is a fluctuating object in disordered systems. PACS numbers: 02.50.-r, 05.20.-y, 05.70.Fh, 64.60.ae, 75.10.-b, 75.10.Hk, 87.10.+e Keywords: statistical physics, magnetism, spin glass, neural networks
We apply the real space renormalization group (RG) to the replica Hamiltonian of the two dimensional Ising Edwards–Anderson model to discuss the existence of the spin glass (SG) phase. We derive the RG equations under the replica symmetric (RS) ansatz and the resulting flow diagram indicates the existence of the SG phase. The critical exponent for the SG transition has a plausible value while that of the multicritical point (MCP) is a complex number. We consider that this failure at the MCP is due to not taking the RS breaking into account. Indeed we find that the RS breaking parameter is relevant both at the SG critical point and the MCP, indicating the nontriviality of the SG phase of this model.
Abstract In recent years scale invariant scattering theory provided the first exact access to the magnetic critical properties of two-dimensional statistical systems with quenched disorder. We show how the theory extends to the overlap variables entering the characterization of spin glass properties. The resulting exact fixed point equations yield both the magnetic and, for the first time, the spin glass renormalization group fixed points. For the case of the random bond Ising model, on which we focus, the spin glass subspace of solutions is found to contain a line of fixed points. We discuss the implications of the results for Ising spin glass criticality and compare with the available numerical results.