Influence of field on frustrations in low-dimensional magnets

Abstract

On the base of exact analytical solutions for maximum eigenvalue of Kramers–Wannier transfer matrix the phenomena of frustrations appearance and suppression of phase transition or, on the contrary, the phase transition appearance and suppression of frustrations are studied on the base of exact analytical solutions for 1D Ising model, 3-state, and 4-state standard Potts models with allowance for the interactions between nearest J and next-nearest neighbors J′, for 6-state and 8-state modified Potts models with allowance for the interaction between only nearest neighbors J. In all the models investigated we obtained exact numbers and values of frustrating fields depending, in particular, on mutual orientation of the field and spin directions.In 2D case on the example of Ising model we studied these phenomena by the numerical replica Monte Carlo method, taking into account the interactions only between nearest neighbors J and an external magnetic field of arbitrary value.We formulated the notion of thermodynamic order parameter and obtained the expressions for the entropy and heat capacity in terms of this order parameter. We also introduced the notion of frustration degree in tight connection with the order parameter. It is shown that when passing across any frustration point (either in presence or absence of magnetic field) cardinal changes of magnetic structure take place in a system.