Estimation of the partition functions of two-dimensional nearest neighbour Ising models

Employing the exact solution of Onsager for two-dimensional Ising models, simple expressions are proposed for computing the partition function, magnetization, specific heat and susceptibility for non-zero magnetic fields of square lattices. The partition function in zero fields is also estimated and excellent agreement with the values arising from the exact solution of Onsager is demonstrated.Comment: 10 pages, 5 Table

Two-dimensional Ising model in a finite magnetic field for the square lattice of infinite sites-Partition function and Magnetization

The partition function and magnetization equations are derived for the two-dimensional nearest neighbour Ising models in a magnetic field.Comment: 5 page

Partition function for the two-dimensional square lattice Ising model in a non-zero magnetic field-A heuristic analysis

The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions estimated from the present analysis are identical with those arising from Onsager's exact solution.Comment: 5 pages;1Figur

Partition Function for Two-Dimensional Nearest Neighbour Ising Model in a Non-Zero Magnetic Field for a Square Lattice of 16 Sites

An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of sixteen sites. The critical temperature is shown to be in excellent agreement with the reported values while the corresponding dimensionless magnetic field is obtained as 0.004.Comment: 14 pages, 3 Figure

Non-Equilibrium Thermodynamics formalism for Marcus cross-exchange electron transfer reaction rates

The cross-exchange electron transfer expression arising from Marcus theory is deduced using Onsager's non-equilibrium Thermodynamics formalism.Comment: 9 page

Enumeration of Hamiltonian walks in two and three dimensional lattices

We report an efficient methodology for enumerating the Hamiltonian walks in two and three dimensional lattices of large sizes, using the concept of centroids. This strategy, with the help of JAVA programming enables the exact computation of the Hamiltonian walks for square and simple cubic lattices. These estimates are useful in designing the protein sequences using hydrophobic-polar lattice models as well as in the analysis of secondary structures in compact polymers.Comment: 28 pages, 2 Figure

Partition functions of two-dimensional Ising models -- A perspective from Gauss hypergeometric functions

Employing heuristic susceptibility equations in conjunction with the well-known critical exponents, the magnetization and partition function for two-dimensional nearest neighbour Ising models are formulated in terms of the Gauss hypergeometric functions. The isomorphism existing between the Bragg-Williams approximation and the exact solution of Onsager is pointed out. The precise manner in which the critical exponents influence the partition functions is pointed out.Comment: 10 page

Partition function for two-dimensional nearest neighbour Ising model in the presence of external magnetic field

The partition function for two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived . A comparison with the partition functions predicted by Onsager is carried out. The critical temperature estimated by two different methods yields good agreement with the result of Yang and Lee.Comment: 4 pages;one Figure; References added to the earlier versio

An Exact Result for the Partition Function of Two-Dimensional Nearest Neighbour Ising Models in Non-Zero Magnetic Field

The partition function of two-dimensional nearest neighbour Ising models in a non-zero magnetic field is derived employing a matrix formulation.Comment: 7 pages, 3 figure

A topological perspective into the sequence and conformational space of proteins

The precise sequence of aminoacids plays a central role in the tertiary structure of proteins and their functional properties. The Hydrophobic-Polar lattice models have provided valuable insights regarding the energy landscape. We demonstrate here the isomorphism between the protein sequences and designable structures for two and three dimensional lattice proteins of very long aminoacid chains using exact enumerations and intuitive considerations.We emphasize that the topological arrangement of the aminoacid residues alone is adequate to deduce the designable and non-designable sequences without explicit recourse to energetics and degeneracies. The results indicate the computational feasibility of realistic lattice models for proteins in two and three dimensions and imply that the fundamental principle underlying the designing of structures is the connectivity of the hydrophobic and polar residues.Comment: 35 pages; 12 Figures and 6 Table