Exact Solution and Correlation Functions of Generalized Double Ising Chains

TL;DR

This paper provides an exact analytical solution for a generalized double-chain Ising model with multi-spin interactions, deriving key thermodynamic quantities and analyzing phase behavior and correlation functions.

Contribution

It introduces explicit formulas for the transfer matrix eigenvalues and eigenvectors, and solves for the model's thermodynamics and correlations in both finite and infinite systems.

Findings

Exact expressions for partition function and free energy.

Analysis of ground states and phase diagram features.

Behavior of correlation functions near frustration points.

Abstract

In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental thermodynamic characteristics of the system. The main results include exact expressions for the partition function, free energy, internal energy, specific heat capacity, magnetization, susceptibility, and entropy in a strip of finite length and in the thermodynamic limit. The work provides explicit formulas for the eigenvalues and shows structure of eigenvectors of the transfer matrix. The expression for magnetization in the thermodynamic limit using components of normalized eigenvector corresponding to the maximum eigenvalue is obtained. A detailed analysis is conducted for a special case of interactions involving all kinds of two- and four-spin interactions. This gives the simplified formula for free energy, it is calculated using the root of quadratic equation. Using special relation between parameters the solution for gonihedric model on the plane is obtained. The research reveals properties of the system, including specific features of ground states and phase diagram characteristics. Particular attention is given to the behavior of physical quantities near frustration points and the investigation of spin correlation functions. Plots of physical characteristics, including inverse correlation length, illustrating the obtained results are constructed.