\eta-Exponents in the one dimensional antiferromagnetic Heisenberg model with next to nearest neighbour coupling

TL;DR

This paper studies the critical exponents related to singularities in the structure factors of a one-dimensional antiferromagnetic Heisenberg model with both nearest and next-nearest neighbor interactions, under an external magnetic field.

Contribution

It introduces a detailed analysis of the critical exponents (,M) and (,M) in the context of the model with next-nearest neighbor coupling and external field.

Findings

Determines the behavior of critical exponents (,M) and (,M) across different parameters.

Provides insights into the singularities in structure factors for the model.

Enhances understanding of phase transitions in one-dimensional antiferromagnetic systems.

Abstract

We investigate the critical exponents $\eta_3(\alpha,M), \eta_1(\alpha,M)$ associated with the singularities in the longitudinal and transverse structure factors of the one dimensional antiferromagnetic Heisenberg model with nearest (J_1) and next to nearest (J_2) neighbour coupling of relative strength $\alpha = {J_2}/{J_1}$ and an external field $B$ with magnetization $M(B)$.