Tag: Ising model

Categories
Equilibrium Statistical Physics

Ground state collapse at strong coupling

R. Hilfer

Journal MESA 8, 307-310 (2017)

submitted on
Friday, May 26, 2017

The infinite range Ising model is usually investigated in the weak coupling limit. Here the model is solved with ferromagnetic coupling at fixed and finite strength. Exact analytical expressions are found for the thermodynamic potentials as functions of enthalpy and external field. These results differ from the potentials for the weak coupling limit. The model shows a temperature driven first order phase transition from a paramagnetic phase at high temperatures into a low temperature phase from which thermal fluctuations are absent.



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Categories
Critical phenomena Equilibrium Statistical Physics

Are Critical Finite Size Scaling Functions Calculable From Knowledge of an Appropriate Critical Exponent ?

R. Hilfer, N.B.Wilding

J. Phys. A: Math. Gen. 28, L281 (1995)
10.1088/0305-4470/28/10/001

submitted on
Tuesday, December 6, 1994

Critical finite size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions the universal part of critical finite size scaling functions has been derived by employing a scaling limit which differs from the traditional finite size scaling limit. In this paper the analytical predictions are compared with Monte Carlo simulation results. We find good agreement between the analytical expression and the simulation results. The agreement is consistent with the possibility that the functional form of the critical finite size scaling function for the order parameter distribution is determined uniquely by only a few universal parameters, most notably the equation of state exponent.



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