SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 49: Critical Phenomena and Phase Transitions

DY 49.8: Vortrag

Donnerstag, 30. März 2023, 17:00–17:15, ZEU 160

Partition function zeros in the 3D Blume-Capel model — •Leïla Moueddene, Ralph Kenna, Nikolaos Fytas, and Bertrand Berche — Laboratoire de Physique et Chimie Théoriques, Université de Lorraine, Vandoeuvre-lès-Nancy, France

The phase diagram of the three-dimensionnal Blume Capel model shows an ordered ferromagnetic phase and a disordered paramagnetic phase, separated by a transition line from second order to first order at the tricritical point (TCP). The universality class of the second-order line is the Ising class, while the tricritical universality class governs the behaviour of the critical exponents at the tricritical point. It is well known that the upper critical dimension is d_uc=3 at the TCP, thus Mean Field exponents are expected, modified by logarithmic correction factor. We determine analytically the logarithmic-correction exponents - also universal - using RG for φ₆ model. The knowledge of the partition function zeros is a quite fundamental and powerful approach to study a phase transition. While the Fisher zeros and Lee-Yang zeros are well known to study the thermal exponent y_t and magnetic exponent y_h, we build a new type of zeros from the complex plane of the crystal field which leads to the crystal exponent y₂: the crystal field zeros. We study the leading and logartihmic-corrections exponents numerically from the partition function zeros and compare with the analytical results, and check if the scaling relations are verified.