The Double-Peak Specific Heat in the Two Dimensional J1–J2 3-State Clock Model

Abstract

By the extensive tensor network algorithms, the J1–J2 3-state clock model is investigated. We focus on the case of J1 > 0, J2 < 0, in which the double-peak structure appears in the curve of the specific heat Cv versus the temperature T. The four parameters \(J_{2} = - 0.2, - 0.8, - 1.4, - 2\) are chosen for the detailed numerical simulation in unit of J1 = 1. The mismatch of peak position between entanglement entropy (EE) and Cv suggests the existence of two Berezinskii–Kosterlitz–Thouless (BKT) phase transitions in case of \(J_{2} = - 0.2, - 0.8\), where the peaks of EE lie inbetween the double peaks of Cv. In the case of J2 = −1.4, the first-peak temperature of Cv and of EE are very close. With further increasing of |J2|, the sequence of the first peak swaps, i.e., the first peak of EE arises at a lower temperature than of Cv. We believe that there is a critical |J2|, above which the first peak of Cv does not correspond to the BKT phase transition. The location offset of the second peak between EE and Cv becomes smaller with |J2| increasing. In addition, the double-peak structure of the specific heat still holds when |J2| is large enough.