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28 relations: Bessel function, Boltzmann distribution, Classical Heisenberg model, Cluster expansion, Goldstone boson, Griffiths inequality, Hagen Kleinert, Helium, Ising model, Jean Ginibre, Kosterlitz–Thouless transition, Lattice model (physics), Magnetization, Mermin–Wagner theorem, N-vector model, Normalizing constant, Order and disorder, Partition function (statistical mechanics), Periodic boundary conditions, Potts model, Statistical mechanics, Superfluid film, Thermodynamic beta, Thermodynamic free energy, Thermodynamic limit, Topological defect, Unit vector, Upper and lower bounds.
Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions of Bessel's differential equation for an arbitrary complex number, the order of the Bessel function.
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Boltzmann distribution
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution, probability measure, or frequency distribution of particles in a system over various possible states.
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Classical Heisenberg model
The Classical Heisenberg model is the n.
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Cluster expansion
In statistical mechanics, the cluster expansion (also called the high temperature expansion or hopping expansion) is a power series expansion of the partition function of a statistical field theory around a model that is a union of non-interacting 0-dimensional field theories.
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Goldstone boson
In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries.
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Griffiths inequality
In statistical mechanics, the Griffiths inequality, sometimes also called Griffiths–Kelly–Sherman inequality or GKS inequality, named after Robert B. Griffiths, is a correlation inequality for ferromagnetic spin systems.
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Hagen Kleinert
Hagen Kleinert (born 15 June 1941) is Professor of Theoretical Physics at the Free University of Berlin, Germany (since 1968), at the West University of Timişoara, at the in Bishkek.
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Helium
Helium (from lit) is a chemical element with symbol He and atomic number 2.
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Ising model
The Ising model, named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics.
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Jean Ginibre
Jean Ginibre is a French mathematical physicist, known for his contributions to random matrix theory (see circular law), statistical mechanics (see FKG inequality, Ginibre inequality), and partial differential equations.
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Kosterlitz–Thouless transition
The Berezinskii–Kosterlitz–Thouless transition (BKT transition) is a phase transition in the two-dimensional (2-D) XY model.
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Lattice model (physics)
In physics, a lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or spacetime.
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Magnetization
In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material.
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Mermin–Wagner theorem
In quantum field theory and statistical mechanics, the Mermin–Wagner theorem (also known as Mermin–Wagner–Hohenberg theorem, Mermin–Wagner–Berezinskii theorem, or Coleman theorem) states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions.
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N-vector model
In statistical mechanics, the n-vector model or O(n) model is a simple system of interacting spins on a crystalline lattice.
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Normalizing constant
The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics.
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Order and disorder
In physics, the terms order and disorder designate the presence or absence of some symmetry or correlation in a many-particle system.
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Partition function (statistical mechanics)
In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium.
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Periodic boundary conditions
Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a unit cell.
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Potts model
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice.
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Statistical mechanics
Statistical mechanics is one of the pillars of modern physics.
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Superfluid film
Superfluidity and superconductivity are macroscopic manifestations of quantum mechanics.
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Thermodynamic beta
In statistical mechanics, the thermodynamic beta (or occasionally perk) is the reciprocal of the thermodynamic temperature of a system.
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Thermodynamic free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform.
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Thermodynamic limit
The thermodynamic limit, or macroscopic limit, of a system in statistical mechanics is the limit for a large number N of particles (e.g., atoms or molecules) where the volume is taken to grow in proportion with the number of particles.
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Topological defect
In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution.
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Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
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Upper and lower bounds
In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (K, ≤) is an element of K which is greater than or equal to every element of S. The term lower bound is defined dually as an element of K which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
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References
[1] https://en.wikipedia.org/wiki/Classical_XY_model
