INTEGRATION OF THE PARTITION FUNCTION OF THREE-DIMENSIONAL ISING MODEL

1987 ◽  
pp. 74-164
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Three Dimensional

scholarly journals Order-disorder statistics. I

1949 ◽  
Vol 196 (1044) ◽  
pp. 36-50 ◽  
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Infinite Matrix ◽  
Characteristic Structure ◽  
Single Function ◽  
Simple Characteristic ◽  
Distant Neighbour ◽  
Function Of Two Variables

In 1941 Kramers & Wannier discussed the statistical mechanics of a two-dimensional Ising model of a ferromagnetic. By making use of a ‘screw transformation’ they showed that the partition function was the largest eigenvalue of an infinite matrix of simple characteristic structure. In the present paper an alternative method is used for deriving the partition function, and this enables the ‘screw transformation’ to be generalized to apply to a number of problems of classical statistical mechanics, including the three-dimensional Ising model. Distant neighbour interactions can also be taken into account. The relation between the ferromagnetic and order-disorder problems is discussed, and it is shown that the partition function in both cases can be derived from a single function of two variables. Since distant neighbour interactions can be taken into account the theory can be formally applied to the statistical mechanics of a system of identical particles.

Zeros of Partition Function and Critical Exponents of the 3D Diluted Ising Model

2016 ◽  
Vol 845 ◽  
pp. 150-153
Author(s):  
Andrey N. Vakilov
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Partition Function ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Three Dimensional ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Zeros Of Partition Function

We used a Monte Carlo simulation of the structurally disordered three dimensional Ising model. For the systems with spin concentrations p = 0.95 ,0.8, 0.6 and 0.5 we calculated the correlation-length critical exponent ν by finite-size scaling. Extrapolations to the thermodynamic limit yield ν(0.95) = 0.705(5) ,ν(0.8) = 0.711(6),ν(0.6) = 0.736(6) and ν(0.5) = 0.744(6). These results are compatible with some previous estimates from a variety of sources. The analysis of the results demonstrates the nonuniversality of the critical behavior in the disordered Ising model.

Accurate estimate ofνfor the three-dimensional Ising model from a numerical measurement of its partition function

1987 ◽  
Vol 59 (7) ◽  
pp. 803-806 ◽  
Author(s):  
Gyan Bhanot ◽  
Román Salvador ◽  
Steve Black ◽  
Paul Carter ◽  
Raúl Toral
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Three Dimensional ◽  
Accurate Estimate

scholarly journals Exact Solution for Three-Dimensional Ising Model

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1837
Author(s):  
Degang Zhang
Keyword(s):  
Boundary Condition ◽  
Ising Model ◽  
Partition Function ◽  
Operator Algebras ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Critical Temperatures ◽  
Cubic Crystal ◽  
Infinite Crystal ◽  
Analytical Expressions

The three-dimensional Ising model in a zero external field is exactly solved by operator algebras, similar to the Onsager’s approach in two dimensions. The partition function of the simple cubic crystal imposed by the periodic boundary condition along two directions and the screw boundary condition along the third direction is calculated rigorously. In the thermodynamic limit an integral replaces a sum in the formula of the partition function. The critical temperatures, at which order–disorder transitions in the infinite crystal occur along three axis directions, are determined. The analytical expressions for the internal energy and the specific heat are also presented.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

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