Finite N analysis of matrix models for n-Ising spin on a random surface

TL;DR

This paper analyzes finite N effects in matrix models for n-Ising spins on random surfaces, deriving critical points and exponents through finite N scaling, and studying small N behavior for one- and two-matrix models.

Contribution

It introduces finite N analysis methods for matrix models of n-Ising spins on random surfaces, providing new insights into critical phenomena and small N behavior.

Findings

Finite N scaling relations for critical points and exponents

Detailed analysis of one- and two-matrix models

Characterization of small N behavior in n-Ising models

Abstract

The saddle point equation described by the eigenvalues of N by N Hermitian matrices is analized for a finite N case and the scaling relation for the large N is considered. The critical point and the critical exponents of matrix model are obtained by the finite N scaling. One matrix model and two matrix model are studied in detail. Small N behavior for n-Ising model on a random surface is investigated.