Topological phase transitions in liquid crystals -- Transiciones de fase topol\'ogicas en cistales l{'\i}quidos

TL;DR

This study provides evidence of a topological phase transition in two-dimensional liquid crystals through Monte Carlo simulations, revealing a low-temperature quasi-long-range order phase with a correlation exponent linearly dependent on temperature, challenging existing theories.

Contribution

The paper demonstrates the existence of a topological phase transition in 2D liquid crystals using advanced simulation techniques, highlighting the relevance of spin waves in systems with non-abelian symmetry.

Findings

Presence of a paramagnetic phase at high temperatures.

Identification of a quasi-long-range order phase at low temperatures.

Correlation function exponent varies linearly with temperature.

Abstract

By means of Monte Carlo simulations, using finite size scaling and conformal transformations, evidences of a topological phase transition in liquid crystals in two dimensions are reported. A paramagnetic phase appears at high temperature whereas a quasi-long-range-order (QLRO) phase is founded at low temperatures. It is determined that the correlation function exponent, at very low temperatures, is linear with the temperature, a typical behavior of spin waves. This contradicts predictions that for systems with non-abelian group of global symmetry the spin waves are not relevant. Aditionally, the implications that would have the presence of impurities in this type of transitions is discussed. ----- Mediante simulaciones de Monte Carlo, utilizando escalamiento de tama\~no finito y transformaciones conforme, se reportan evidencias de una transici\'on de fase topol\'ogica en cristales l{\'\i}quidos en dos dimensiones. A altas temperaturas se presenta una fase paramagn\'etica mientras que a bajas temperaturas se encuentra un fase de cuasi-largo-orden (QLRO). Se encuentra que a muy bajas temperaturas el exponente de la funci\'on de correlaci\'on de la fase QLRO es lineal con la temperatura teni\'endose de esta manera un comportamiento t{\'\i}pico de ondas de esp{\'\i}n. Esto \'ultimo contradice predicciones de que para sistemas con grupo de simetr{\'\i}a global no abeliano las ondas de esp{\'\}n no son relevantes. Adicionalmente se discute que implicaciones tendr{\'\i}a la presencia de impurezas en este tipo de transiciones.