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M. V. Sangaranarayanan

Publications and source records attributed to M. V. Sangaranarayanan.

9 recordsLinked to original sources
arXiv2019

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.

cond-mat.stat-mech↗
arXiv2015

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.

q-bio.BM↗
arXiv2010

Estimation of Magnetization, Susceptibility and Specific heat for the two-dimensional Ising Model in a Non-zero Magnetic field

The partition functions for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for finite square lattices with the help of graph theoretical procedures, show-bit algorithm, enumeration of configurations and transfer matrix methods. A new recurrence relation valid for all lattice sizes is proposed. A novel method of computing the critical temperature has been demonstrated. The magnetization and susceptibility for infinite lattices in the presence of magnetic field is estimated. The critical exponent δ pertaining to the magnetization has also been computed.

cond-mat.stat-mech↗
arXiv2007

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.

cond-mat.stat-mech↗