Study of the Blume-Capel model through the partition function zeros

Study of the Blume-Capel model through the partition function zeros

Study of the Blume-Capel model through the partition function zeros

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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 $\phi_6$ 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 y_2: 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.

Contact : Leïla Moueddene

Informations complémentaires

Auteur - Leïla Moueddene (Université de Lorraine)

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Date et heure

17 janvier 2023 @ 07:00 PM
 

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