Unveiling Phase Transitions In 1D Systems With Short-Range Interactions

The statement that any phase transition is related to the appearance or disappearance of long-range spatial correlations precludes a finite transition temperature in one-dimensional (1D) systems. In this paper we demonstrate that the 1D Ising model with short-range exchange interactions exhibits a second-order phase transition at a finite temperature relying on the proper choice of the order parameter. To accomplish this, we combined analytical calculations and high-precision entropic sampling simulations and chose a slightly different order parameter, namely the module of the magnetization. Notably, we detected a phase transition with a corresponding critical temperature around 15 K, which is in excellent agreement with experimental results. Our study indicates that an inappropriate choice of the order parameter may mask phase transitions in one-dimensional systems.

A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method

Two-dimensional (2D) square, rectangular and hexagonal lattices and 3D parallelepipedic lattices of spin crossover (SCO) compounds which represent typical examples of first order phase transitions compounds are studied in terms of their size, shape and model through an Ising-like Hamiltonian in which the fictitious spin states are coupled via the respective short and long-range interaction parameters J, and G. Furthermore, an environmental L parameter accounting for surface effects is also introduced. The wealth of SCO transition properties between its bi-stable low spin (LS) and high spin (HS) states are simulated using Monte Carlo Entropic Sampling (MCES) method which favors the scanning of macro states of weak probability occurrences. For given J and G, the focus is on surface effects through parameter L. It is shown that the combined first-order phase transition effects of the parameters of the Hamiltonian can be highlighted through two typical temperatures, TO.D., the critical order-disorder temperature and Teq the equilibrium temperature that is fixed at zero effective ligand field. The relative positions of TO.D. and Teq control the nature of the transition and mediate the width and position of the thermal hysteresis curves with size and shape. When surface effects are negligible (L = 0), the equilibrium transition temperature, Teq. becomes constant, while the thermal hysteresis’ width increases with size. When surface effects are considered, L ≠ 0, Teq. increases with size and the first order transition vanishes in favor of a gradual transition until reaching a threshold size, below which a reentrance phenomenon occurs and the thermal hysteresis reappears again, as shown for hexagonal configuration.

Thermodynamic properties of rod-like chains: Entropic sampling simulations

In this work, we apply entropic sampling simulations to a three-state model which has exact solutions in the microcanonical and grand-canonical ensembles. We consider N chains placed on an unidimensional lattice, such that each site may assume one of the three states: empty (state 1), with a single molecule energetically null (state 2), and with a single molecule with energy [Formula: see text] (state 3). Each molecule, which we will treat here as dimers, consists of two monomers connected one to each other by a rod. The thermodynamic properties such as internal energy, densities of dimers and specific heat were obtained as functions of temperature, where the analytic results in the microcanonical and grand-canonical ensembles were successfully confirmed by the entropic sampling simulations.