# Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture

@article{Takeda2005ExactLO, title={Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture}, author={Koujin Takeda and Tomohiro Sasamoto and Hidetoshi Nishimori}, journal={Journal of Physics A}, year={2005}, volume={38}, pages={3751-3774} }

We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems to derive formulae which make it possible to understand all the relevant available numerical results in a unified way. The method applies to non-self-dual lattices as well as to self-dual cases, in the former case of which we derive a relation for a pair of…

## 24 Citations

Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices

- Physics
- 2006

A conjecture is given for the exact location of the multicritical point in the phase diagram of the ± J Ising model on the triangular lattice. The result p c =0.8358058 agrees well with a recent…

Analytical evidence for the absence of spin glass transition on self-dual lattices

- Physics
- 2009

We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality…

Multicritical point relations in three dual pairs of hierarchical-lattice Ising spin glasses

- Physics
- 2005

The Ising spin glasses are investigated on three dual pairs of hierarchical lattices, using exact renormalization-group transformation of the quenched bond probability distribution. The goal is to…

Multicritical points for spin-glass models on hierarchical lattices.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

An improved conjecture is proposed to give more precise predictions of the multicritical points than the conventional one, inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data.

Location and properties of the multicritical point in the Gaussian and ±J Ising spin glasses

- Physics
- 2009

We use transfer-matrix and finite-size scaling methods to investigate the location and properties of the multicritical point of two-dimensional Ising spin glasses on square, triangular, and honeycomb…

Locations of multicritical points for spin glasses on regular lattices.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

A systematic technique is proposed, by an improved technique, giving more precise locations of the multicritical points on the square, triangular, and hexagonal lattices by carefully examining the relationship between two partition functions related with each other by the duality.

Properties of the multicritical point of ±J Ising spin glasses on the square lattice

- Physics
- 2006

nl /, with the help of finite-size scaling and conformal invariance concepts. Our results are c = 0.461; 0.187 0.196; / = 1.7975; nl / = 5.592. A direct evaluation of correlation functions on the…

Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model

- Physics
- 2007

We consider the three-dimensional $\pm J$ model defined on a simple cubic
lattice and study its behavior close to the multicritical Nishimori point where
the paramagnetic-ferromagnetic, the…

Duality analysis on random planar lattices.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This paper presents a fascinating result associated with optimal error thresholds for a class of quantum error correction code, the surface code on the random planar lattice, which is known as a skillful technique to protect the quantum state.

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