Eur. Phys. J. B 51, 321-329 (2006)
https://doi.org/10.1140/epjb/e2006-00226-6

Analysis of a long-range random field quantum antiferromagnetic Ising model

¹ Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata, 700064, India
² Complex Systems Engineering, Graduate School of Information Science and Technology, Hokkaido University, N14-W9, Kita-ku, Sapporo, 060-0814, Japan

Corresponding authors: ^a bikask.chakrabarti@saha.ac.in - ^b arnab.das@saha.ac.in - ^c j_inoue@complex.eng.hokudai.ac.jp

Received: 21 February 2006
Published online: 13 June 2006

Abstract

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions and random fields on each site following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.