arXiv subjects

Purushottam D. Gujrati

Publications and source records attributed to Purushottam D. Gujrati.

3 recordsLinked to original sources

arXiv2019

Phase transitions of antiferromagnetic Ising spins on the zigzag surface of an asymmetrical Husimi lattice

An asymmetrical 2D Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice, which we have previously applied to study polymers near a surface. The model retains the advantages of simple formulation and exact calculation of the conventional Bethe-like lattices. An antiferromagnetic Ising model is solved on the surface of this lattice to evaluate thermal properties such as free energy, energy density and entropy, from which we have successfully identified a first order order-disorder transition other than the spontaneous magnetization, and a secondary transition on the supercooled state indicated by the Kauzmann paradox.

cond-mat.stat-mech↗

arXiv2014

The Thermodynamic Behaviors and Glass Transition on the Surface/Thin Film of An Ising Spin Model on Recursive Lattice

A quasi 2-dimensional recursive lattice formed by planar elements have been designed to investigate the surface thermodynamics of Ising spin glass system with the aim to study the metastability of supercooled liquids and the ideal glass transition. The lattice is constructed as a hybrid of partial Husimi lattice representing the bulk and 1D single bonds representing the surface. The recursive properties of the lattices were adopted to achieve exact calculations. The model has an anti-ferromagnetic interaction to give rise to an ordered phase identified as crystal, and a metastable solution representing the amorphous/metastable phase. Interactions between particles farther away than the nearest neighbor distance are taken into consideration. Free energy and entropy of the ideal crystal and supercooled liquid state of the model on the surface are calculated by the partial partition function. By analyzing the free energies and entropies of the crystal and supercooled liquid state, we are able to identify the melting transition and the second order ideal glass transition on the surface. The results show that due to the coordination number change, the transition temperature on the surface decreases significantly compared to the bulk system. Our calculation agrees with experimental and simulation results on the thermodynamics of surfaces and thin films conducted by others.

cond-mat.stat-mech↗

arXiv2014

Thermodynamic Comparison and the Ideal Glass Transition of A Monatomic Systems Modeled as an Antiferromagnetic Ising Model on Husimi and Cubic Recursive Lattices of the Same Coordination Number

Two kinds of recursive lattices with the same coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states. The Ising model with multi-particle interactions is designed to represent a monatomic system or an alloy. Two solutions of the model exhibit the crystallization of liquid, and the ideal glass transition of supercooled liquid respectively. Based on the solutions, the thermodynamics on both lattices was examined. In particular, the free energy, energy, and entropy of the ideal glass, supercooled liquid, crystal, and liquid state of the model on each lattice were calculated and compared with each other. Interactions between particles farther away than the nearest neighbor distance are taken into consideration. The two lattices show comparable properties on the transition temperatures and the thermodynamic behaviors, which proves that both of them are practical to describe the regular 3-D case, while the different effects of the unit types are still obvious.

cond-mat.stat-mech↗