相关论文: Lectures on the Spin and Loop $O(n)$ Models

In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…

Relations between the mean values of distributions of flipped spins on periodic Heisenberg XX chain and some aspects of enumerative combinatorics are discussed. The Bethe vectors, which are the state-vectors of the model, are considered…

We exactly reformulate the lattice CP(N-1) spin model on a D dimensional torus as a loop model whose configurations correspond to the complete set of strong coupling graphs of the original system. A Monte Carlo algorithm is described and…

Fully packed loop models on the square and the honeycomb lattice constitute new classes of critical behaviour, distinct from those of the low-temperature O(n) model. A simple symmetry argument suggests that such compact phases are only…

Dynamics of interaction of topological solitons (vortices) in (2+1)-dimensional O(3) nonlinear sigma model in anisotropic case are investigated. By numerical simulation methods is shown that the changes of rotation frequency of isotopic…

The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1>1/2). A new effective field theory describing the long…

We study multilevel fermions in an optical lattice described by the Hubbard model with on site SU($n$)-symmetric interactions. We show that in an appropriate parameter regime this system can be mapped onto a spin model with all-to-all…

We study the spin n-point functions of the planar Ising model on a simply connected domain \Omega discretised by the square lattice \delta\mathbb{Z}^{2} under near-critical scaling limit. While the scaling limit on the full-plane \mathbb{C}…

Phase transitions of the mixed spin-1/2 and spin-S (S >= 1/2) Ising model on a three-dimensional (3D) decorated lattice with a layered magnetic structure are investigated within the framework of a precise mapping relationship to the simple…

We prove Griffiths inequalities for the $O(N)$-spin model with inhomogeneous coupling constants and external magnetic field for any $N\geq 2$. This is achieved by using a representation of $O(N)$-spins in terms of random paths that reduces…

We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length $n$. The machinery necessary to model physics is then developed by considering correlations between base-2…

A unidirectional "density" wave order in an otherwise isotropic environment is guaranteed to display a smecticlike Goldstone mode. Examples of such "soft" states include conventional smectic liquid crystals, putative…

We present results of our Monte Carlo simulation of the Ising-O(3) model on the two-dimensional (2D) and quasi-2D lattices. This model is an effective classical model for the stacked square-lattice $J_1$-$J_2$ Heisenberg model where the…

We present conjectured exact expressions for two types of correlations in the dense O$(n=1)$ loop model on $L\times \infty$ square lattices with periodic boundary conditions. These are the probability that a point is surrounded by $m$ loops…

Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…

The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon…

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the kagom\'e lattice are studied for the exactly solvable infinite-component spin-vector model, D \to \infty. In this limit, the critical coupling…

A Green-function theory for the dynamic spin susceptibility in the square-lattice spin-1/2 antiferromagnetic compass-Heisenberg model employing a generalized mean-field approximation is presented. The theory describes magnetic long-range…

The static transverse and longitudinal correlation functions (CF) of a 3-dimensional ferromagnet are calculated for the exactly solvable anisotropic spherical model (ASM) determined as the limit D \to \infty of the classical D-component…