The Ising Model
The dimension of physical systems. Usual three-dimensional systems are associated with a certain class of critical exponents. There are experimental realizations of two-dimensional systems, whose critical behavior is characterized by another class of distinct and well-defined critical exponents.
The dimension of the order parameter. For simple fluids and uniaxial ferromagnets, the order parameter is a scalar number. For an isotropic ferromagnet, the critical parameter is a three-dimensional vector.
The range of the microscopic interactions. For most systems of physical interest, the microscopic interactions are of short range. We will see that statistical systems with long-range microscopic interactions lead to the set of classical critical exponents.
KeywordsIsing Model Transfer Matrix Critical Exponent Thermodynamic Limit Cayley Tree
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