Related papers: Topological order in matrix Ising models
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the…
We study a model of two-dimensional interacting monomers which has two symmetric absorbing states and exhibits two kinds of phase transition; one is an order-disorder transition and the other is an absorbing phase transition. Our focus is…
Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated (Villain) transverse-field Ising model on the square lattice. We consider a "primary" spin order parameter and a "secondary" dimer order…
Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations in directions perpendicular and parallel to the ordering wave-vector even above the magnetic…
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…
A harmonic oscillator linearly coupled with a linear chain of Ising spins is investigated. The $N$ spins in the chain interact with their nearest neighbours with a coupling constant proportional to the oscillator position and to $N^{-1/2}$,…
The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We…
Ordered phases of matter, such as solids, ferromagnets, superfluids, or quantum topological order, typically only exist at low temperatures. Despite this conventional wisdom, we present explicit local models in which all such phases persist…
The ferromagnetic Ising model on an $n\times n$ square lattice region $\Lambda$ with mixed boundary conditions can exhibit a phase transition as temperature varies. For this spin system, if we fix the spins on the top and bottom sides of…
Using Monte Carlo simulations we study the two-dimensional Ising model on triangular, square, and hexagonal lattices with various topologies. We focus on the behavior of the magnetic susceptibility and of the specific heat near the critical…
We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse…
We investigate the critical properties of the phase transition towards complex tensor order that has been proposed to occur in spin-orbit coupled superconductors. For this purpose we formulate the bosonic field theory for fluctuations of…
The Onsager algebra, invented to solve the two-dimensional Ising model, can be used to construct conserved charges for a family of integrable $N$-state chiral clock models. We show how it naturally gives rise to a "pivot" procedure for this…
The matrix product structure is considered on a regular lattice in the hyperbolic plane. The phase transition of the Ising model is observed on the hyperbolic $(5, 4)$ lattice by means of the corner-transfer-matrix renormalization group…
We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas…
Numerous experiments have reported discrete symmetry breaking in the high temperature pseudogap phase of the hole-doped cuprates, including breaking of one or more of lattice rotation, inversion, or time-reversal symmetries. In the absence…
We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in…
We investigate the ground-state properties of a disorderd Ising model with uniform transverse field on the Bethe lattice, focusing on the quantum phase transition from a paramagnetic to a glassy phase that is induced by reducing the…
The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the…
Material realization of the non-Abelian Kitaev spin liquid phase - an example of Ising topological order (ITO) - has been the subject of intense research in recent years. The $4d$ honeycomb Mott insulator $\alpha$-RuCl$_3$ has emerged as a…