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Real Space Renormalization Group Analysis with the Replica Method for the Two Dimensional Ising Edwards–Anderson Model

Takehisa Hasegawa, Koji Nemoto

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.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.

Journal of the Physical Society of JapanJun 29, 20061 citation

REAL SPACE RENORMALIZATION GROUP ANALYSIS WITH THE REPLICA METHOD FOR THE TWO-DIMENSIONAL ISING SPIN GLASS

T. HASEGAWA, K. NEMOTO

International Symposium on Topological Aspects of Critical Systems and NetworksJun 1, 20070 citations

Real space renormalization group calculations for the 3-dimensional Ising model

J. Oitmaa, Michael N. Barber

Physica B+CJan 1, 19774 citations

Topologically invariant tensor renormalization group method for the Edwards-Anderson spin glasses model

Chuang Wang, Shao-Meng Qin, Haijun Zhou

Tensor renormalization group (TRG) method is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the two-dimensional Edwards-Anderson model, by a new topological invariant TRG scheme. We propose an approach to calculate the local magnetizations and nearest pair correlations simultaneously. The Nishimori multicritical point predicted by the topological invariant TRG agrees well with the recent Monte Carlo results. The TRG schemes outperform the mean-field methods on the calculation of the partition function. We notice that it might obtain a negative partition function at sufficiently low temperatures. However, the negative contribution can be neglected if the system is large enough. This topological invariant TRG can also be used to study three-dimensional spin glass systems.Tensor renormalization group (TRG) method is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the two-dimensional Edwards-Anderson model, by a new topological invariant TRG scheme. We propose an approach to calculate the local magnetizations and nearest pair correlations simultaneously. The Nishimori multicritical point predicted by the topological invariant TRG agrees well with the recent Monte Carlo results. The TRG schemes outperform the mean-field methods on the calculation of the partition function. We notice that it might obtain a negative partition function at sufficiently low temperatures. However, the negative contribution can be neglected if the system is large enough. This topological invariant TRG can also be used to study three-dimensional spin glass systems.

Physical Review BNov 10, 201423 citations

Real space renormalization group study of the two-dimensional super-antiferromagnetic Ising model

Isabel Cristina Souza Dinóla, A. Saguia, B. Boechat

Physics Letters AMar 15, 20094 citations

Phase diagrams of bond Ising models

A. Benyoussef, N. Boccara

Real space renormalisation group techniques and the replica method of Edwards and Anderson (1975), combined with successive variational approximations going beyond mean field, are used to calculate phase diagrams of various Ising systems. For a bond dilute 2D Ising model with nearest-neighbour interactions, real-space renormalisation group techniques provide very precise results which are used to test the reliability of the replica method. Combined with variational approximations going beyond mean field, this last method is applied to 3D Ising models with competing nearest-neighbour and next-nearest-neighbour interactions.Real space renormalisation group techniques and the replica method of Edwards and Anderson (1975), combined with successive variational approximations going beyond mean field, are used to calculate phase diagrams of various Ising systems. For a bond dilute 2D Ising model with nearest-neighbour interactions, real-space renormalisation group techniques provide very precise results which are used to test the reliability of the replica method. Combined with variational approximations going beyond mean field, this last method is applied to 3D Ising models with competing nearest-neighbour and next-nearest-neighbour interactions.

Journal of Physics C Solid State PhysicsMar 10, 19829 citations

Real Space Renormalization Group Analysis with the Replica Method for the Two Dimensional Ising Edwards-Anderson Model(Condensed matter: electronic structure and electrical, magnetic, and optical properties)

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Real Space Renormalization Group Analysis with the Replica Method for the Two Dimensional Ising Edwards-Anderson Model(Condensed matter: electronic structure and electrical, magnetic, and optical properties)

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