# Finite size and finite temperature studies of the $osp(1|2)$ spin chain

## TL;DR

This paper investigates the finite size and temperature properties of an $osp(1|2)$ quantum spin chain, deriving integral equations to analyze its critical behavior and thermodynamics, including specific heat and magnetic susceptibility.

## Contribution

It introduces non-linear integral equations for the transfer matrix eigenvalues of the $osp(1|2)$ spin chain, enabling detailed analysis of its finite size scaling and thermodynamic properties.

## Key findings

- Determined the central charge and its effective value at low temperatures.
- Numerically evaluated specific heat and magnetic susceptibility.
- Results agree with existing literature predictions.

## Abstract

We study a quantum spin chain invariant by the superalgebra $osp(1|2)$. We derived non-linear integral equations for the row-to-row transfer matrix eigenvalue in order to analyze its finite size scaling behaviour and we determined its central charge. We have also studied the thermodynamical properties of the obtained spin chain via the non-linear integral equations for the quantum transfer matrix eigenvalue. We numerically solved these NLIE and evaluated the specific heat and magnetic susceptibility. The analytical low temperature analysis was performed providing a different value for the effective central charge. The computed values are in agreement with the numerical predictions in the literature.