The free energy singularity of the asymmetric six-vertex model and the excitations of the asymmetric XXZ chain

Albertini, Giuseppe; Dahmen, Sílvio R.; Wehefritz, Birgit

doi:10.1016/s0550-3213(97)00078-3

Cited by 21 publications

(28 citation statements)

References 26 publications

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“…An analogous result, with δv ↔ δh was reached in [8], but only for the two points b = ±γ, where the tangent to Γ is parallel to the v-axis…”

Section: δV = V T H T δHsupporting

confidence: 57%

“…Notice that c 1 = 0 if b = ±γ. This case was dealt with in [8]. The solution is For the field, after using (8) and (11) −4i…”

Section: It Turns Out That λmentioning

confidence: 99%

“…These expansions reduce to those of [8] when b → ±γ (the limit should be taken in the elliptic functions because several series are not convergent when |b| = γ). No term δb n appears in (24), and that had to be expected since the line a = π (i.e.…”

Section: It Turns Out That λmentioning

confidence: 99%

“…If one treats the problem with the transfer matrix method, an exact solution is provided by the Bethe-ansatz [1,2,3]. The phase diagram was outlined in the original paper [1], while further developments came more recently [2,5,6,7,8] (the list is not exhaustive. Papers dealing with the ferroelectric regime are not included).…”

Section: Introductionmentioning

confidence: 99%

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Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

Albertini

1998

Journal of Statistical Physics

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The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines δv = kδh, where (δh, δv) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski-Talapov transition δf ∼ const(δh) 3/2 for any direction other than the tangential one. In the latter case δf shows a discontinuity in the third derivative.

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“…An analogous result, with δv ↔ δh was reached in [8], but only for the two points b = ±γ, where the tangent to Γ is parallel to the v-axis…”

Section: δV = V T H T δHsupporting

confidence: 57%

“…Notice that c 1 = 0 if b = ±γ. This case was dealt with in [8]. The solution is For the field, after using (8) and (11) −4i…”

Section: It Turns Out That λmentioning

confidence: 99%

Section: It Turns Out That λmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

Albertini

1998

Journal of Statistical Physics

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“…Albertini et al 6 pointed out that E(λ s 1 , λ s 2 ) vanishes at λ s 1 = λ s 2 = ±π/γ + i. The momentum p(λ s 1 , λ s 2 ) at this point is p(λ s 1 , λ s 2 ) = ±π + i γ + 2…”

Section: Summary and Discussionmentioning

confidence: 98%

A Non-Hermitian Critical Point and the Correlation Length of Strongly Correlated Quantum Systems

Nakamura

Hatano

2006

J. Phys. Soc. Jpn.

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We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. In a previous article, we conjectured that the non-Hermitian critical point where the energy gap vanishes is equal to the inverse correlation length of the Hermitian system and we confirmed the conjecture for two exactly solvable systems. In this article, we present more evidence for the conjecture.We also argue the basis of our conjecture by noting the dispersion relation of the elementary excitation.

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Reaction–Diffusion Processes from Equivalent Integrable Quantum Chains

Henkel¹,

Orlandini

Santos³

1997

Annals of Physics

105

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One-dimensional reaction diffusion systems are mapped through a similarity transformation onto integrable (and a priori nonstochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The reaction diffusion processes related to free fermion systems with site-independent interactions are classified. The time-dependence of the mean particle density is calculated. Furthermore, new integrable stochastic processes related to the Heisenberg XXZ chain are identified and the relaxation times for the particle density and density correlation for these systems are found.1997 Academic Press

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The free energy singularity of the asymmetric six-vertex model and the excitations of the asymmetric XXZ chain

Cited by 21 publications

References 26 publications

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

A Non-Hermitian Critical Point and the Correlation Length of Strongly Correlated Quantum Systems

Reaction–Diffusion Processes from Equivalent Integrable Quantum Chains

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