Evidence of Kosterlitz-Thouless phase transitions in the Ising model with dipolar interactions

Abstract

The ferromagnetic bidimensional Ising model with dipolar interactions has been proposed to model ultrathin films with strong out-of-plane anisotropy. The phase diagram presents a rich phenomenology that includes lowtemperature phases characterized by stripes of width n (h n ) and a high-temperature phase with domains of stripes with mutually perpendicular orientations, named tetragonal liquid (TL). The latter phase can be reached by two possible ways. One of them is the direct transition h n to TL, and the other one is through an intermediate phase with orientational order but short-range positional disorder, named nematic phase (NM). The regions of the phase diagram where these transitions occur, as well as their character, remain an open question and are the object of the present work. In order to clarify this topic, intensive Monte Carlo simulations were performed by employing short-time dynamics as the main tool for studying the phase transition behavior. The dynamic evolution of the orientational order parameter and its moments are measured for selected values of the ratio between the ferromagnetic exchange and dipolar constants, called δ. The obtained results indicate that the intermediate NM phase is present for δ 2 in narrow ranges of temperatures. Also, the results suggest that both transitions, i.e., h n -NM and NM-TL, have a Kosterlitz-Thouless character. This type of topological transition is observed in continuous bidimensional models and have been proposed for discrete ones, as in the case of the present work.

Influence of ion structure and solvent electric dipole on ultrananoporous supercapacitor: a lattice model study

“…Frequently, one would rather give up quantitative accuracy requirement and wishes the theoretical methods tractable and give qualitatively correct change tendency. Ising model [59][60][61][62][63][64][65][66][67][68] is well suitable for this purpose. Although the Ising model is essentially based on discrete lattice concept [69], it plays an important role in our understanding [69][70][71][72][73][74] of behaviors of the real systems which are usually modeled by continuous classical statistical model and are too complex to be treated in a friendly way.…”