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We numerically investigate two-dimensional systems of hard rectangles at constant pressure through extensive hard-particle Monte Carlo simulations. We determine the complete phase diagram as a function of packing fraction and aspect ratio,…
The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between…
The model of localized fermions on the triangular lattice is analyzed in means of the Monte Carlo simulations in the grand canonical ensemble. The Hamiltonian of the system has a form of the extended Hubbard model (at the atomic limit) with…
We present a new scenario for the breakdown of ferromagnetic order in a two-dimensional quantum magnet with competing ferromagnetic and antiferromagnetic interactions. In this, dynamical effects lead to the formation of two-magnon bound…
The rich mesophase polymorhism and the phase sequence of board-like colloids depends critically on their shape anisometry. Implementing extensive Monte Carlo simulations, we calculated the full phase diagram of sterically interacting…
We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm,…
We present a method for simulating fluid vesicles with in-plane orientational ordering. The method involves computation of local curvature tensor and parallel transport of the orientational field on a randomly triangulated surface. It is…
The bent-core liquid crystals (LCs) are highly regarded as the next-generation materials for electro-optic devices. The nematic (N) phase of these LCs possesses highly ordered smectic-like cybotactic clusters which are promising in terms of…
Competition between short- and long-range interactions underpins many emergent phenomena in nature. Despite rapid progress in their experimental control, computational methods capable of accurately simulating open quantum many-body systems…
Monte Carlo simulations are used to show that the steady state of the d=2, two-temperature, diffusive XY model displays a continuous phase transition from a homogeneous disordered phase to a phase with long-range order. The long-range order…
We study the extended Hubbard model on the triangular lattice as a function of filling and interaction strength. The complex interplay of kinetic frustration and strong interactions on the triangular lattice leads to exotic phases where…
The structure of nematic liquid crystals formed by bent-core mesogens (BCMs) is studied in the context of Monte Carlo simulations of a simple molecular model that captures the symmetry, shape and flexibility of achiral BCMs. The results…
Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science and…
A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied by a mesoscopic theory and by MC simulations. We assume hard-cores of the same size for both components, short-range attraction long-range…
The extended Hubbard model in the atomic limit, which is equivalent to lattice $S=1/2$ fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard $U$ interaction and both nearest-neighbor ($W_{1}$) and…
Phase diagram and pattern formation in two-dimensional Ising model with coupling between order parameter and lattice vibrations is investigated by Monte-Carlo simulations. It is shown that if the coupling is strong enough (or phonons are…
We realize and study the ionic Hubbard model using an interacting two-component gas of fermionic atoms loaded into an optical lattice. The bipartite lattice has honeycomb geometry with a staggered energy-offset that explicitly breaks the…
A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J_1 between the first…
Tailoring the performance of next-generation high entropy materials requires a deep understanding of the competition between entropy-driven random solid solution and enthalpy-driven chemical ordering. Investigating such order and disorder…
Recent experiments report that the long looked for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations we concentrate on some elementary…