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Importantly, transfer matrix methods allow to tackle probabilistic lattice models from an algebraic perspective, allowing for instance the use of results from representation theory. As an example of observables that can be calculated from this method, the probability of a particular state occurring at position x is given by:
An ice-type model is a lattice model defined on a lattice of coordination number 4. That is, each vertex of the lattice is connected by an edge to four "nearest neighbours". A state of the model consists of an arrow on each edge of the lattice, such that the number of arrows pointing inwards at each vertex is 2.
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. [1] By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenomena of solid-state physics.
The existence of the thermodynamic limit for the free energy and spin correlations were proved by Ginibre, extending to this case the Griffiths inequality. [3]Using the Griffiths inequality in the formulation of Ginibre, Aizenman and Simon [4] proved that the two point spin correlation of the ferromagnetics XY model in dimension D, coupling J > 0 and inverse temperature β is dominated by (i.e ...
In statistical mechanics, the two-dimensional square lattice Ising model is a simple lattice model of interacting magnetic spins. The model is notable for having nontrivial interactions, yet having an analytical solution. The model was solved by Lars Onsager for the special case that the external magnetic field H = 0. [1]
As with the ice-type models, the eight-vertex model is a square lattice model, where each state is a configuration of arrows at a vertex.The allowed vertices have an even number of arrows pointing towards the vertex; these include the six inherited from the ice-type model (1-6), sinks (7), and sources (8).
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, [1] chemistry, neuroscience, [2] computer science, [3] [4] information theory [5] and ...
The quantum Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically.
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