The Exact Determination of the Critical Points for 2-D Square Lattice Ising Model with the Nearest and Next Nearest Neighbors Interactions

2011 ◽  
Vol 8 (3) ◽  
pp. 872-878 ◽  
Author(s):  
S. Ranjbar
Keyword(s):  
Ising Model ◽  
Critical Points ◽  
Nearest Neighbors ◽  
Square Lattice ◽  
Exact Determination

CRITICAL SPIN-1 VERTEX MODELS AND O(n) MODELS

1990 ◽  
Vol 04 (05) ◽  
pp. 929-942 ◽  
Author(s):  
Bernard NIENHUIS
Keyword(s):  
Critical Points ◽  
Critical Exponents ◽  
Square Lattice ◽  
Two Dimensional ◽  
Planar Lattice ◽  
Vertex Models ◽  
Critical Manifold ◽  
Multicritical Points ◽  
Straightforward Generalization

A method is presented by which critical and multicritical points of spin-1 (three-state) vertex models and classical O(n) models on two-dimensional lattices are determined. It is a straightforward generalization of the ideas that earlier led to the determination of critical points and critical exponents of a honeycomb O(n) model. On the square lattice the methods leads to tricritical as well as critical loci. For n=2 a larger critical manifold is found than for other values of n. At the critical and multicritical points thus produced the models turn out to be soluble. The method is applicable to O(n) models and spin-1 vertex models on any planar lattice.

Frustrations and Phase Transitions in Ising Model on 2D Lattices

2010 ◽  
Vol 168-169 ◽  
pp. 435-438 ◽  
Author(s):  
Felix A. Kassan-Ogly ◽  
B.N. Filippov ◽  
V.V. Men’shenin ◽  
Akai K. Murtazaev ◽  
M.K. Ramazanov ◽  
...  
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Method ◽  
Ising Model ◽  
Analytical Solutions ◽  
Nearest Neighbors ◽  
Square Lattice ◽  
Maximum Eigenvalue ◽  
Exact Analytical Solutions

The problem of frustrations and phase transition appearance or suppression is studied on the base of exact analytical solutions for maximum eigenvalue of Kramers-Wannier transfer matrix in the Ising model on a square lattice [1], a triangular and honeycomb lattices [2], and kagome lattice [3] with allowance for the interactions between nearest J is studied. We also studied these phenomena by the numerical “replica Monte Carlo method”, taking also into account the interactions between next-nearest neighbors J'.

scholarly journals III. Further experiments on the vapour densities of potassium and sodium

1879 ◽  
Vol 29 (196-199) ◽  
pp. 490-493 ◽  
Keyword(s):  
Considerable Error ◽  
Exact Determination ◽  
The Way

In one former communication “On the Vapour Densities of Potas­sium and Sodium,” we pointed out the chief obstacles which lay in the way of an exact determination of these constants. Having overcome the chief manipulative difficulties in connexion with the method we described, there still remained the problem for solution as to how far the use of iron bottles in our experiments might affect the results. If the iron retained the metals or allowed their vapours to diffuse with rapidity through it, a considerable error might be produced without its being easily detected.

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