Critical properties of the Izergin-Korepin and solvable O(n) models and their related quantum spin chains

Warnaar, S. Ole; Batchelor, Murray T.; Nienhuis, Bernard

doi:10.1088/0305-4470/25/11/016

Cited by 82 publications

(200 citation statements)

References 30 publications

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“…In this paper we study by means of Monte Carlo simulation the semi-flexible VISAW polymer model precisely at the BN-point. We find estimates for the exponents, and hence the scaling dimensions, that are in harmony with those found by Foster and Pinettes [1] and at variance with those predicted by Warnaar et al [10] .…”

Section: Introductionsupporting

confidence: 91%

“…Some agreement and some discrepancy with the scaling dimensions proposed [7,8,9,10] was found in [14] and a first order nature to the transition was conjectured. Very recently Foster and Pinettes [1] have used transfer matrices and the Density Matrix Renormalisation Group Method (DMRG) to consider the bulk and surface exponents of these models.…”

Section: Introductionmentioning

confidence: 83%

“…For this model five critical branches are exactly known [7,8,9,10]. In one of these branches (named 'branch 0' in [7]) straight segments are completely suppressed and it can be shown that in this case the model maps to the ISAW model on the Manhattan lattice for which the conjectured exponents are ν = 4/7, γ = 6/7 [11,12,13].…”

Section: Introductionmentioning

confidence: 94%

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Numerical simulation of a lattice polymer model at its integrable point

Bedini¹,

Owczarek²,

Prellberg³

2013

J. Phys. A: Math. Theor.

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Abstract. We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Blöte and Nienhuis in J. Phys. A. 22, 1415Phys. A. 22, (1989 and it describes polymers with some attraction, providing thus a model for the polymer collapse transition. At a particular set of Boltzmann weights the model is integrable and the exponents ν = 12/23 ≈ 0.522 and γ = 53/46 ≈ 1.152 have been computed via identification of the scaling dimensions x t = 1/12 and x h = −5/48. We directly investigate the polymer scaling exponents via Monte Carlo simulations using the PERM algorithm. By simulating this polymer model for walks up to length 4096 we find ν = 0.576(6) and γ = 1.045(5), which are clearly different from the predicted values. Our estimate for the exponent ν is compatible with the known θ-point value of 4/7 and in agreement with very recent numerical evaluation by Foster and Pinettes [1].

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Section: Introductionsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 83%

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Numerical simulation of a lattice polymer model at its integrable point

Bedini¹,

Owczarek²,

Prellberg³

2013

J. Phys. A: Math. Theor.

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“…One of the reasons why the stability of the DS fixed point has previously been a vexed question is that the traditional Coulomb gas [45] approach to loop models hides the SU(N ) symmetry: This prevents us from being able to classify and count perturbations. (Other sources of confusion have included the assumption that the DS exponents are the same as those of de Gennes's tricritical O(n → 0) model, which we will argue is not the case, and the existence of various other solvable fixed points that were candidates for the θ point [5,[46][47][48]. ) The σ model is the right formulation, as we have seen.…”

Section: Perturbing the Honeycomb Modelmentioning

confidence: 97%

Universality class of the two-dimensional polymer collapse transition

Nahum

2016

Phys. Rev. E

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The nature of the θ point for a polymer in two dimensions has long been debated, with a variety of candidates put forward for the critical exponents. This includes those derived by Duplantier and Saleur for an exactly solvable model. We use a representation of the problem via the CP N−1 σ model in the limit N → 1 to determine the stability of this critical point. First we prove that the Duplantier-Saleur (DS) critical exponents are robust, so long as the polymer does not cross itself: They can arise in a generic lattice model and do not require fine-tuning. This resolves a longstanding theoretical question. We also address an apparent paradox: Two different lattice models, apparently both in the DS universality class, show different numbers of relevant perturbations, apparently leading to contradictory conclusions about the stability of the DS exponents. We explain this in terms of subtle differences between the two models, one of which is fine-tuned (and not strictly in the DS universality class). Next we allow the polymer to cross itself, as appropriate, e.g., to the quasi-two-dimensional case. This introduces an additional independent relevant perturbation, so we do not expect the DS exponents to apply. The exponents in the case with crossings will be those of the generic tricritical O(n) model at n = 0 and different from the case without crossings. We also discuss interesting features of the operator content of the CP N−1 model. Simple geometrical arguments show that two operators in this field theory, with very different symmetry properties, have the same scaling dimension for any value of N (or, equivalently, any value of the loop fugacity). Also we argue that for any value of N the CP N−1 model has a marginal odd-parity operator that is related to the winding angle.

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“…The previously-studied sequence (1.1), (1.2) is picked out by the monotonicity of the function c eff as a function of r. In all other cases, somewhat to our surprise, we found that the effective central charge undergoes a number of oscillations as it interpolates between its short and long distance limits. Our approach differs from the TBA method, and is much closer to that of the papers [20][21][22][23][24][25][26], in that a single nonlinear integral equation (NLIE) is proposed to describe infinitely-many different perturbed conformal field theories, each being picked out by an appropriate choice of certain parameters. For massless flows, the one previous example of such an equation was found by Al.…”

Section: Introductionmentioning

confidence: 99%

New families of flows between two-dimensional conformal field theories

2000

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We present evidence for the existence of infinitely-many new families of renormalisation group flows between the nonunitary minimal models of conformal field theory. These are associated with perturbations by the φ 21 and φ 15 operators, and generalise a family of flows discovered by Martins. In all of the new flows, the finitevolume effective central charge is a non-monotonic function of the system size. The evolution of this effective central charge is studied by means of a nonlinear integral equation, a massless variant of an equation recently found to describe certain massive perturbations of these same models. We also observe that a similar nonmonotonicity arises in the more familiar φ 13 perturbations, when the flows induced are between nonunitary minimal models.

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Critical properties of the Izergin-Korepin and solvable O(n) models and their related quantum spin chains

Cited by 82 publications

References 30 publications

Numerical simulation of a lattice polymer model at its integrable point

Numerical simulation of a lattice polymer model at its integrable point

Universality class of the two-dimensional polymer collapse transition

New families of flows between two-dimensional conformal field theories

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