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The Hamiltonian of the one-dimensional Ising model on a lattice of L sites with free boundary conditions is = =, …, +, where J and h can be any number, since in this simplified case J is a constant representing the interaction strength between the nearest neighbors and h is the constant external magnetic field applied to lattice sites.
The Ising model, a mathematical model in statistical mechanics, is utilized to study magnetic phase transitions and is a fundamental model of interacting systems. [1] Constructing an irreducible Markov chain within a finite Ising model is essential for overcoming computational challenges encountered when achieving exact goodness-of-fit tests ...
In d=2, the two-dimensional critical Ising model's critical exponents can be computed exactly using the minimal model,. In d=4, it is the free massless scalar theory (also referred to as mean field theory). These two theories are exactly solved, and the exact solutions give values reported in the table.
The transverse field Ising model is a quantum version of the classical Ising model.It features a lattice with nearest neighbour interactions determined by the alignment or anti-alignment of spin projections along the axis, as well as an external magnetic field perpendicular to the axis (without loss of generality, along the axis) which creates an energetic bias for one x-axis spin direction ...
The critical Ising model is the critical point of the Ising model on a hypercubic lattice in two or three dimensions. It has a Z 2 {\displaystyle \mathbb {Z} _{2}} global symmetry, corresponding to flipping all spins.
Analytical results can be theoretically achieved in mean field theory in high dimensions or when exact solutions are known such as the two-dimensional Ising model. The theoretical treatment in generic dimensions requires the renormalization group approach or, for systems at thermal equilibrium, the conformal bootstrap techniques.
massless Schwinger model; supersymmetric sine-Gordon model; supersymmetric sinh-Gordon model; conformal minimal models; critical Ising model; tricritical Ising model; 3-state Potts model; various perturbations of conformal minimal models; superconformal minimal models; Wess–Zumino–Witten model; Nonlinear Schroedinger equation; Korteweg–de ...
The three-state Potts CFT, also known as the parafermion CFT, is a conformal field theory in two dimensions. It is a minimal model with central charge = /.It is considered to be the simplest minimal model with a non-diagonal partition function in Virasoro characters, as well as the simplest non-trivial CFT with the W-algebra as a symmetry.