The <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>XY</mi></math></span> Model Has Long-Range Order for All Spins and All Dimensions Greater than One

Tom Kennedy; Elliott H. Lieb; B. Sriram Shastry

doi:10.1103/PhysRevLett.61.2582

The $XY$ Model Has Long-Range Order for All Spins and All Dimensions Greater than One

Tom Kennedy, Elliott H. Lieb, and B. Sriram Shastry

Phys. Rev. Lett. 61, 2582 – Published 28 November 1988

Abstract

The quantum $XY$ model of interacting spins on a hypercubic lattice has long-range order in the ground state for all values of the spin and all dimensions greater than one. We also show that in the limit of high dimension the spontaneous magnetization converges to the spontaneous magnetization of the Néel state.

Received 13 July 1988

DOI:https://doi.org/10.1103/PhysRevLett.61.2582

Authors & Affiliations

Tom Kennedy^*, Elliott H. Lieb, and B. Sriram Shastry^†

Department of Physics, Princeton University, P.O. Box 708, Princeton, New Jersey 08544

^*Permanent address: Mathematics Department, University of Arizona, Tucson, AZ 85721.
^†On leave from Tata Institute of Fundamental Research, Bombay, India; now at AT&T Bell Laboratories, Murray Hill, NJ 07974.