Spin matrix elements in 2D Ising model on the finite lattice

TL;DR

This paper derives explicit formulas for all spin matrix elements in the finite 2D Ising model on a periodic lattice, extending previous results and validating them through transfer matrix calculations.

Contribution

It provides a comprehensive set of explicit formulas for spin matrix elements in the finite 2D Ising model, generalizing prior results and confirming their accuracy with transfer matrix tests.

Findings

Explicit formulas for all spin matrix elements

Generalization of previous results to finite lattices

Validation through transfer matrix calculations

Abstract

We present explicit formulas for all spin matrix elements in the 2D Ising model with the nearest neighbor interaction on the finite periodic square lattice. These expressions generalize the known results [Phys. Rev. D19, (1979), 2477--2479; hep-th/0107117; hep-th/0112167] (coincide with them in the appropriate limits) and fulfill the test of straightforward transfer matrix calculations for finite $N$.