Finite size effects around pseudo-transition in one-dimensional models with nearest neighbor interaction

TL;DR

This paper investigates finite size effects in one-dimensional quantum spin models exhibiting pseudo-transitions, revealing how peaks in thermodynamic functions behave with system size and clarifying their non-divergent nature.

Contribution

It provides a detailed analysis of finite size effects on pseudo-transitions in 1D models, including empirical fitting functions and insights into peak behavior as system size varies.

Findings

Peaks in specific heat and susceptibility become sharper and taller with increasing system size.

Peak heights approach a finite limit in the thermodynamic limit, indicating no true phase transition.

An empirical function effectively models the finite size behavior of thermodynamic peaks.

Abstract

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.