Tricritical exponents for trails on a square lattice obtained by the scanning simulation method

Meirovitch, Hagai; Lim, Hwa A.

doi:10.1103/physreva.38.1670

Cited by 35 publications

(21 citation statements)

References 28 publications

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“…In contrast, in the ISAW model a tricritical (θ) point is found in the phase diagram. Therefore, the fact that the collapse transition is of bicritical nature found here is in agreement with several works on square lattice showing that the universality classes of the collapse transition of the ISAT and the ISAW models are different [19][20][21][22][23].…”

Section: Thermodynamic Properties Of the Model On The Bethe Latticesupporting

confidence: 93%

“…This model presents a very rich phase diagram when the parameter space is increased by including stiffness [18], so that the chains are semi-flexible. In contrast, for the more general ISAT model, where the trails are allowed to cross themselves, there are no exact results and the nature of its collapse transition is a subject of long debate in literature: while some works present evidences of continuous collapse transition in BN [19] or "undetermined" [20][21][22][23] universality classes, the possibility of a discontinuous transition was also suggested in [24]. It seems to be no surprise that the inclusion of crossings in the BN model apparently makes it no longer exactly solvable and may lead to richer phase diagrams.…”

Section: Introductionmentioning

confidence: 99%

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Nature of the collapse transition in interacting self-avoiding trails

Stilck

2016

Phys. Rev. E

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We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination q and on a Husimi lattice built with squares and coordination q=4. The exact grand-canonical solutions of the model are obtained, considering that up to K monomers can be placed on a site and associating a weight ω_{i} with an i-fold visited site. Very rich phase diagrams are found with nonpolymerized, regular polymerized, and dense polymerized phases separated by lines (or surfaces) of continuous and discontinuous transitions. For a Bethe lattice with q=4 and K=2, the collapse transition is identified with a bicritical point and the collapsed phase is associated with the dense polymerized (solidlike) phase instead of the regular polymerized (liquidlike) phase. A similar result is found for the Husimi lattice, which may explain the difference between the collapse transition for ISATs and for interacting self-avoiding walks on the square lattice. For q=6 and K=3 (studied on the Bethe lattice only), a more complex phase diagram is found, with two critical planes and two coexistence surfaces, separated by two tricritical and two critical end-point lines meeting at a multicritical point. The mapping of the phase diagrams in the canonical ensemble is discussed and compared with simulational results for regular lattices.

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Section: Thermodynamic Properties Of the Model On The Bethe Latticesupporting

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Nature of the collapse transition in interacting self-avoiding trails

Stilck

2016

Phys. Rev. E

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“…The Boltzmann weight is a product over terms for each node. Denoting the two outgoing links at a given node by o,o and the two incoming links by i,i , we have (14) where Tr denotes the integral over the Zs with the length constraint. Note that the two terms at each node correspond to the two ways of pairing up the links at that node shown in Fig.…”

Section: Completely Packed Modelmentioning

confidence: 99%

“…The best studied model with crossings is the collapse point of the interacting self-avoiding trail [12][13][14][15][16]23,24]. This model is in many ways analogous to the honeycomb lattice model solved by Duplantier and Saleur.…”

Section: Introductionmentioning

confidence: 99%

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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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Polymer Collapse

Nahum¹

2014

Springer Theses

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Tricritical exponents for trails on a square lattice obtained by the scanning simulation method

Cited by 35 publications

References 28 publications

Nature of the collapse transition in interacting self-avoiding trails

Nature of the collapse transition in interacting self-avoiding trails

Universality class of the two-dimensional polymer collapse transition

Polymer Collapse

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