Locations of multicritical points for spin glasses on regular lattices

Abstract

We present an analysis leading to precise locations of the multicritical points for spin glasses on regular lattices. The conventional technique for determination of the location of the multicritical point was previously derived using a hypothesis emerging from duality and the replica method. In the present study, we propose a systematic technique, by an improved technique, giving more precise locations of the multicritical points on the square, triangular, and hexagonal lattices by carefully examining relationship between two partition functions related with each other by the duality. We can find that the multicritical points of the $\pm J$ Ising model are located at $p_c=0.890813$ on the square lattice, where $p_c$ means the probability of $J_{ij}=J(>0)$, at $p_c=0.835985$ on the triangular lattice, and at $p_c=0.932593$ on the hexagonal lattice. These results are in excellent agreement with recent numerical estimations.

17pages, this is the published version with some minnor corrections. Previous title was "Precise locations of multicritical points for spin glasses on regular lattices"

References in corpus (5)

• Multicritical points for the spin glass models on hierarchical lattices
• Strong disorder fixed points in the two-dimensional random-bond Ising model
• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
• Multicritical Point Relations in Three Dual Pairs of Hierarchical-Lattice Ising Spin-Glasses
• Multicritical Points of Potts Spin Glasses on the Triangular Lattice

Cited by in corpus (4)

• Error Threshold for Color Codes and Random 3-Body Ising Models
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
• Excitations of the bimodal Ising spin glass on the brickwork lattice