Related papers: Numerical study of a transition between Z2 topolog…

We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…

Spontaneous symmetry breaking is well understood through the classical "Mexican Hat" picture, which describes many quantum phases of matter. Recently, several new classes of quantum phases of matter, such as topological orders and symmetry…

The string-net approach by Levin and Wen and the local unitary transformation approach by Chen, Gu and Wen provided ways to systematically label non-chiral topological orders in 2D. In those approaches, different topologically ordered…

We present new results for the ordering process of a two-dimensional Ising model with anisotropic frustrating next-nearest-neighbor interactions. We concentrate on a specific wide temperature and parameter region to confirm the existence of…

The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…

We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of…

The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…

Finding suitable indicators for characterizing quantum phase transitions plays an important role in understanding different phases of matter. It is especially important for fracton phases where a combination of topology and…

We consider the weakly first order phase transition between the isotropic and ordered phases of nematics in terms of the behavior of topological line defects. Analytical and Monte Carlo results are presented for a new coarse-grained lattice…

Topologically ordered phases are gapped states, defined by the properties of excitations when taken around one another. Here we demonstrate a method to extract the statistics and braiding of excitations, given just the set of ground-state…

From consideration of the order-parameter distribution, we propose an observable which makes a clear distinction between true and quasi long-range orders in the two-dimensional generalized $q$-state clock model. Measuring this quantity by…

We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be…

We study transitions between phases of matter with topological order. By studying these transitions in exactly solvable lattice models we show how universality classes may be identified and critical properties described. As a familiar…

In a real system the heating is nonuniform and a second-order phase transition into a broken symmetry phase occurs by propagation of the temperature front. Two parameters, the cooling rate $\tau_Q$ and the velocity $v_T$ of the transition…

Topologically ordered phases exhibit further complexity in the presence of global symmetries: Their anyonic excitations may exhibit different transformation patterns under these symmetries, leading to a classification in terms of…

Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…

We develop a model in the framework of nuclear fragmentation at thermodynamic equilibrium which can be mapped onto an Ising model with constant magnetization. We work out the thermodynamic properties of the model as well as the properties…

Spontaneous symmetry breaking occurs in various equilibrium and nonequilibrium systems, where phase transitions are typically marked by a single critical point that separates ordered and disordered regimes. We reveal a novel phenomenon in…

We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…

We demonstrate that spin-charge separation can occur in two dimensions and note its confluence with superconductivity, topology, gauge theory, and fault-tolerant quantum computation. We construct a microscopic Ising-like model and, at a…