First order phase transition in coupled one dimensional systems

V. N. Bogomolov, E.V. Kolla, Yu. A. Kumzerov

M. Asorey, J. G. Esteve

Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg

Y. Imry, Douglas J. Scalapino, Leon Gunther

The properties of one-dimensional systems with coupled order parameters are investigated. Mean-field results are reviewed, and some essentially exact results, including fluctuatins, are obtained numerically. Our results show the possibility of mixed phases and pseudo-first-order transitions.

Alessandro Campa, Vahan Hovhannisyan, Stefano Ruffo +1 more

Abstract We derive the phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction in the canonical ensemble. The free energy is obtained by mapping the model onto the spin-1 Blume–Emery–Griffiths model and solving it by using a Hubbard–Stratonovich transformation combined with the transfer matrix method. A complex structure with lines of first-order transitions, two triple points and a critical point appears at finite temperature. The phase diagram is two-dimensional, since there are two adjustable parameters, the nearest-neighbour coupling K and the temperature T . We show that the phase diagram does not present second-order phase transition lines, due to the fact that the order parameter is not a symmetry-breaking one. Quite remarkably, we are able to determine analytically one of the first-order phase transition lines. We also prove that, when the nearest-neighbour coupling K is large and negative, the first-order transition temperature becomes asymptotically independent of K .

Jooyoung Lee, Enzo Granato, J. Michael Kosterlitz

We study, by a Migdal-Kadanoff approximation and Monte Carlo simulations, the phase diagram of a two-dimensional coupled XY-Ising model. This model can describe phase transitions in different systems with underlying continuous and ${\mathit{Z}}_{2}$ symmetries. Depending on the parameters, we find separate XY, Ising and first-order transitions. Also, a line of continuous transitions is found with simultaneous loss of XY and Ising order and varying critical exponents. The fully frustrated XY and Josephson-junction systems can be considered to lie along different paths in the model which can result in nonuniversal behavior if the transition is a single one.