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AIP conference proceedings

Ground State and Thermodynamic Properties of the Spin-1 Antiferromagnetic Ising Model on a Δ Chain in Transverse Crystal Fields

Yoshiyuki Fukumoto, Akihide Oguchi

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We study effects of applying a transverse crystal field with strength Γ to the fully frustrated spin‐1 Ising Δ chain with an antiferromagnetic interaction J. Using Oittma and Brasch’s theorem for the ground state wave function of the transverse crystal field Ising models, we show that a ground state with no spontaneous symmetry breaking is stabilized by the transverse crystal field in our system for all Γ/J. The thermodynamic properties are studied numerically, and we found that this system shows a three‐staged entropy release as a function of temperature if J ≫ Γ.

DOI
10.1063/1.2355079

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We study effects of applying a transverse crystal field with strength Γ to the fully frustrated spin‐1 Ising Δ chain with an antiferromagnetic interaction J. Using Oittma and Brasch’s theorem for the ground state wave function of the transverse crystal field Ising models, we show that a ground state with no spontaneous symmetry breaking is stabilized by the transverse crystal field in our system for all Γ/J. The thermodynamic properties are studied numerically, and we found that this system shows a three‐staged entropy release as a function of temperature if J ≫ Γ.
The specific heat of the S = 1 transverse-crystal-field Ising model with an antiferro-magnetic exchange interaction J on a ∆-chain is studied by using the exact-diagonalization, quantum Monte Carlo and finite-temperature Lanczos methods. We find that when the strength of the transverse crystal field Γ is chosen to be sufficiently small, the specific heat exhibits a three-peak structure as a function of temperature, with peaks at T ∼ 0.05Γ, 0.2Γ and 0.7J. In addition to the two energy scales Γ and J, a new energy scale ∼ 0.1 × Γ appears due to the geometrical frustration and the existence of the Sz = 0 states in the present system. Geometrically frustrated spin systems have attracted considerable attention for a long time. It is expected that the introduction of quantum fluctuations into a clas-sically degenerate manifold leads to exotic properties of ground states and thermo-dynamics. From this point of view, S = 1/2 transverse-field Ising antiferromagnets
An antiferromagnetic Ising model on the Δ chain, with a macroscopic ground state degeneracy and exponentially decaying spin correlation functions, is studied. By introducing transverse magnetic fields Γ on spins at tips of the triangles and λΓ on spins on the bottom chain, we study the ground state as a function of λ and Γ. The λ=0 problem is exactly solved and the ground state has a staggered magnetization on the bottom chain for any Γ>0. Because the transverse field on the bottom chain with finite λ destroys the staggered order, the order–disorder transition occurs as λ is increased. We calculate the transition point λ c (Γ/ J ) as a function of Γ/ J , where J denotes the magnitude of the exchange interaction, by using the series expansion method around the λ=0 limit and conclude that λ c (Γ/ J =+0)≃0.9459. It is shown that states in the degenerate ground state manifold at Γ=0 are crucial in getting a finite value of λ c (+0).
The ground-state properties of the triangular antiferromagnetic Ising model with Ising constant J in a transverse field h are investigated by a real-space renormalisation group method. For h=0, the known properties (energy=-J, finite entropy, no order) are recovered. For h not=0, the ground state remains highly degenerate, no order exists and the correlation function exhibits power-law behaviour up to (h/J)c approximately=1.41, where a phase transition takes place to a non-degenerate ground state. At h/J=(h/J)c, power-law behaviour is still observed for the correlation function but with a different exponent. Just above this region a gap Delta opens ( Delta approximately ((h/J)-(h/J)c)s with s=0.8) and the coherence length of the correlation function xi diverges as xi varies as ((h/J)-(h/J)c)-v with v=0.8. This corresponds to a three-dimensional classical model where h is replaced by the temperature. In this type of system, where the ground state has a degeneracy proportional to N2/3 it is predicted that a transition will occur at a finite T c to a low-temperature phase without order but with power-law behaviour for the correlation function, as for the classical XY model in two dimensions.