The Ising phase in the J1-J2 Heisenberg Model

The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1>1/2). A new effective field theory describing the long wavelength physics of the model is derived from the quantu...

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Bibliographic Details
Published inarXiv.org
Main Authors Lante, V, Parola, A
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.02.2006
Subjects
Antiferromagnetism
Couplings
Field theory
Heisenberg theory
Ising model
Magnons
Order parameters
Phase diagrams
Phase transitions
Quantum phenomena
Rotational states
Statistical models
Two dimensional models
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Summary:The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1>1/2). A new effective field theory describing the long wavelength physics of the model is derived from the quantum hamiltonian. The structure of the resulting non linear sigma model allows to recover the known spin wave results in the collinear regime, supports the presence of an Ising phase transition at finite temperature and suggests the possible occurrence of a non-magnetic ground state breaking rotational symmetry. By means of Lanczos diagonalizations we investigate the spin system at T=0, focusing our attention on the region where the collinear order parameter is strongly suppressed by quantum fluctuations and a transition to a non-magnetic state occurs. Correlation functions display a remarkable size independence and allow to identify the transition between the magnetic and non-magnetic region of the phase diagram. The numerical results support the presence of a non-magnetic phase with orientational ordering.
ISSN:2331-8422
DOI:10.48550/arxiv.0602544