The partition function for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for a finite square lattice of 16, 25, 36 and 64 sites with the help of graph theoretical procedures, show-bit algorithm, enumeration of configurations and transfer matrix methods. © Indian Academy of Sciences.

M. V. Sangaranarayanan

Department Of Chemistry

M. Vinothkumar

G. Nandhini

Graph theory

Magnetic fields

Transfer matrix method

FINITE LATTICES

NEAREST NEIGHBOUR

Partition functions

SHOW-BIT ALGORITHMS

SQUARE LATTICES

TWO-DIMENSIONAL ISING MODEL

ZERO MAGNETIC FIELDS

Ising model

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Journal of Chemical Sciences

The partition function for one-dimensional nearest neighbour Ising models is estimated by summing all the energy terms in the Hamiltonian for N sites. The algebraic expression for the partition function is then employed to deduce the eigenvalues of the basic 2 × 2 matrix and the corresponding Hermitian Toeplitz matrix is derived using the Discrete Fourier Transform. A new recurrence relation pertaining to the partition function for two-dimensional Ising models in zero magnetic field is also proposed. © Indian Academy of Sciences.

Partition function of nearest neighbour Ising models: Some new insights

The analysis of two-dimensional condensation of organic compounds at the mercury|aqueous solution interface is carried out using a two-state Ising model formalism. Explicit results for the transition potential in terms of surface coverage, temperature and adsorbate concentration are reported. A methodology for estimating critical temperatures using the classical formula of dispersion forces is proposed, and the calculation of critical concentration is discussed. The estimated critical parameters are compared with the experimental data for various organic adsorbates.

Journal of Electroanalytical Chemistry

Two-dimensional condensation of organic adsorbates at the mercury|aqueous solution interface: A global analysis of critical parameters using ising model formalism

Journal of Statistical Physics

Weighted Graph Colorings

Nature Physics

Melting the double helix

Solid State Communications

Free energies of steps on (111) fcc surfaces

Partition function of the two-dimensional nearest neighbour Ising models for finite lattices in a non-zero magnetic field

Journal	Data powered by TypesetJournal of Chemical Sciences
Publisher	Data powered by TypesetSpringer India
ISSN	09743626
Open Access	Yes