MONTE CARLO METHODS FOR LATTICE SPIN MODELS AND THEIR APPLICATION FOR NUMERICAL SIMULATION OF CRITICAL CASIMIR FORCES

Oleg Vasilyev

Max Planck Institute for Intelligent Systems

The universality hypothesis and the finite size scaling concept form a basis of the modern theory of the second order phase transitions. Monte Carlo simulations of lattice spin models of different universality classes let us to study details of the phase transition and to compute critical indexes and amplitudes of thermodynamic quantities. In the fluctuating media near the critical point (critical binary mixture, liquid helium near the superfluid transition point) long ranged fluctuations of the order parameter arise. These fluctuations produce long-ranged critical Casimir forces acting on confining surfaces or immersed objects. In the first part of the lecture basic algorithms for Monte Carlo simulation of lattice models will be described. In the second part the application of these methods for numerical investigation of the critical Casimir effect will be given.

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