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

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.