Solution of Macroscopic State Equations of Blume-Capel Model Using Nonlinear Dynamics Concepts

Year 2013, Volume: 17 Issue: 1, 53 - 60, 01.04.2013

Asaf Tolga Ülgen Naci Sünel

Abstract

The macroscopic state equations of Blume-Capel Model were solved by using the concepts of nonlinear dynamics. Negative and positive exchange constant values yield bifurcations of pitchfork and subcritical flip types, respectively. Hence, we obtained bifurcations corresponding to second order phase transitions. The critical values of parameters were calculated from the neutral stability condition and the 3-dimensional phase diagram was plotted.

Keywords

Blume-Capel Models, Phase Transitions, Bifurcation, Phase diagram

Blume Capel Modelinin Mikroskopik Durum Denklemlerini Nonlinear Dinamik Kavramları Kullanilarak Çözülmesi

Abstract

The macroscopic state equations of Blume-Capel Model were solved by using the concepts of nonlinear dynamics. Negative and positive exchange constant values yield bifurcations of pitchfork and subcritical flip types, respectively. Hence, we obtained bifurcations corresponding to second order phase transitions. The critical values of parameters were calculated from the neutral stability condition and the 3-dimensional phase diagram was plotted.

Keywords

Blume-Capel Model, Faz Geçişleri, Dallanmalar, Faz Diyagramı

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