Zigzag spin-S chain near ferromagnet-antiferromagnet transition point

TL;DR

This paper investigates the critical behavior of a frustrated ferromagnetic spin chain near a phase transition, revealing quantum effects for spin-1/2 and classical behavior for higher spins through perturbation theory and scaling analysis.

Contribution

It provides a detailed analysis of critical exponents and quantum fluctuations in the spin-S chain near the transition point, highlighting differences between half-integer and integer spins.

Findings

Quantum fluctuations alter critical exponents for s=1/2.

Critical exponents remain classical for s≥1.

Dimerization occurs near the transition in the singlet phase.

Abstract

The properties of the ferromagnetic frustrated spin-S one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state is studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for $s=1/2$ are sufficiently strong to change the classical critical exponents, while for spin systems with $s\geq 1$ the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.