Abstract
The method for calculation of the partition function of lattice model for the magnet in the external field near critical point (CP) is proposed. The recurrence relations and their explicit solution near the critical point are founded. It is shown that dependence on temperature of thermodynamic functions near CP, when the field value comes down to zero, is in good agreement with the previous results obtained using the collective variable method. The phase transition temperature (when h = 0) is calculated and the dependence on parameters of interaction potential is found.
Highlights
A significant progress in the theoretical description of phase transitions on the microscopical level has been achieved using the collective variables (CV) method [1]
The effectiveness of the CV method was demonstrated by applying a one-component three-dimensional spin model [2] to the description of critical behavior
The critical point for one-component spin system is defined at the temperature equal to Tc and in zero external field h
Summary
A significant progress in the theoretical description of phase transitions on the microscopical level has been achieved using the collective variables (CV) method [1]. This approach allows one to take into account the collective behavior which plays a crucial role near the phase transition point. The critical temperature Tc with explicit expressions for thermodynamic functions near Tc have been obtained and their dependence on microscopic parameters of the system was found. The evaluation of expressions for free energy and other thermodynamic functions (heat capacity and order parameter in particular) near Tc in the vanishing external field is of great theoretical and practical interest.
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