相关论文: Geometrical Phase Transitions
An analysis is presented of the phase transition of the quantum Ising model with transverse field on the d-dimensional hypercubic lattice. It is shown that there is a unique sharp transition. The value of the critical point is calculated…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
In a system of interacting thin rigid rods of equal length $2 \ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $\kappa=\ell/a$ and the temperature are varied.…
We use high-temperature series expansions to obtain thermodynamic properties of the quantum compass model, and to investigate the phase transition on the square and simple cubic lattices. On the square lattice we obtain evidence for a phase…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…
We propose a rigorous approach of Semi-Infinite lattice systems illustrated with the study of surface transitions of the semi-infinite Potts model.
Binary magnetic square lattice Ising system with nearest neighbour interactions were simulated using the Monte Carlo technique. Two types of ions were randomly distributed on the lattice sites, one type interacting ferromagnetic and the…
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
The multi-branched Husimi recursive lattice has been extended to a virtual structure with fractional numbers of branches joined on one site. Although the lattice is undrawable in real space, the concept is consistent with regular Husimi…
In these notes, the application of Feynman's sum-over-paths approach to thermal phase transitions is discussed. The paradigm of such a spacetime approach to critical phenomena is provided by the high-temperature expansion of spin models.…
We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the…
The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the…
Hubbard-type models on the hexagonal lattice are of great interest, as they provide realistic descriptions of graphene and other related materials. Hybrid Monte Carlo simulations offer a first-principles approach to study their phase…
We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with…
The differential geometric aspects of Geometric Phases are reviewed.
We discuss the status of recent Gibbsian descriptions of the restriction (projection) of the Ising phases to a layer. We concentrate on the projection of the two-dimensional low temperature Ising phases for which we prove a variational…