Polymer models with competing collapse interactions on Husimi and Bethe lattices

Pretti, Marco

doi:10.1103/physreve.93.032110

Cited by 8 publications

(9 citation statements)

References 50 publications

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“…Rich phase diagrams were found in these studies, with the coil-globule transition for four-coordinated cases (which are mean-field approximations for the square lattice) being associated with a bicritical point. Such behavior was confirmed in a recent study by Pretti [18], where the ISAT model was generalized by including an attractive interaction between NN monomers on single occupied sites not linked by a polymer bond and solved on Bethe and Husimi lattices with q = 4. The VISAW model (when the crossings are forbidden and NN interactions vanish), the SASAW (when crossings and collisions are not allowed), the model by Wu and Bradley [19] (when collisions and crossings have the same weight) and the simple ISAT model (when the NN interaction vanishes) are recovered as particular cases.…”

Section: Introductionsupporting

confidence: 58%

“…The three transition lines meet at z = τ x = 1, as may be seen in Eq. (18). As ω → 0, at the discontinuous AN-NP transition line, located at z = 1, the NP-P critical surface and the P-AN discontinuous critical surface meet, while the DP-P critical surface and the P-AN discontinuous critical surface meet at the DP-AN discontinuous transition line, located at τ x = 1/z.…”

Section: A Phase Diagramsmentioning

confidence: 93%

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Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice

2017

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We consider a model of semiflexible interacting self-avoiding trails (sISATs) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting self-avoiding walks (SASAWs) to investigate the collapse transition of polymers, with the attractive interactions being on site as opposed to nearest-neighbor interactions in SASAWs. The grand-canonical version of the sISAT model is solved on a four-coordinated Bethe lattice, and four phases appear: non-polymerized (NP), regular polymerized (P), dense polymerized (DP), and anisotropic nematic (AN), the last one present in the phase diagram only for sufficiently stiff chains. The last two phases are dense, in the sense that all lattice sites are visited once in the AN phase and twice in the DP phase. In general, critical NP-P and DP-P transition surfaces meet with a NP-DP coexistence surface at a line of bicritical points. The region in which the AN phase is stable is limited by a discontinuous critical transition to the P phase, and we study this somewhat unusual transition in some detail. In the limit of rods, where the chains are totally rigid, the P phase is absent and the three coexistence lines (NP-AN, AN-DP, and NP-DP) meet at a triple point, which is the endpoint of the bicritical line.

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Section: Introductionsupporting

confidence: 58%

Section: A Phase Diagramsmentioning

confidence: 93%

Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice

2017

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“…This suggests that the CEP and TC lines meet at the bi-critical point when ω → 1, showing that this point is actually a multi-critical point. This multi-critical behaviour is consistent with recent results by Pretti [30], who has analysed the flexible model (ω = 1), but considering general τ c = τ x . When ω → 0, the CEP and TC lines also seem to meet at a single multi-critical point, which turns out to be the point where the transition lines (critical discontinuous NP-AN and DP-AN and coexistence NP-DP) meet in phase diagram for rigid rods (ω = 0), discussed in the previous section.…”

Section: 32supporting

confidence: 91%

Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares

Oliveira,

Dantas,

Prellberg

et al. 2017

Preprint

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We study a model of semi-flexible self-avoiding trails, where the lattice paths are constrained to visit each lattice edge at most once, with configurations weighted by the number of collisions, crossings and bends, on a Husimi lattice built with squares. We find a rich phase diagram with five phases: a non-polymerised phase (NP), low density (P1) and high density (P2) polymerised phases, and, for sufficiently large stiffness, two additional anisotropic (nematic) (AN1 and AN2) polymerised phases within the P1 phase. Moreover, the AN1 phase which shows a broken symmetry with a preferential direction, is separated from the P1 phase by the other nematic AN2 phase. Although this scenario is similar to what was found in our previous calculation on the Bethe lattice, where the AN-P1 transition was discontinuous and critical, the presence of the additional nematic phase between them introduces a qualitative difference. Other details of the phase diagram are that a line of tri-critical points may separate the P1-P2 transition surface into a continuous and a discontinuous portion, and that the same may happen at the NP-P1 transition surface, details of which depend on whether crossings are allowed or forbidden. A critical end-point line is also found in the phase diagram.

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“…Similar treelike lattices can be built with triangles, cubes and so on. Recent examples of systems investigated on these Husimi cacti include frustrated magnets [77], polymers [78] and lattice gases [79]. In particular, quite recently binary [80] and ternary [81] mixtures of kNN particles were analyzed by us on a HL built with cubes.…”

Section: B Husimi Lattice Solutionsmentioning

confidence: 99%

Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases

Rodrigues,

Oliveira

2021

Preprint

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Although lattice gases composed by kNN particles, forbidding up to their kth nearest neighbors of being occupied, have been widely investigated in literature, the location and the universality class of the fluid-columnar transition in the 2NN model on the square lattice is still a topic of debate. Here, we present grand-canonical solutions of this model on Husimi lattices built with diagonal square lattices, with 2L(L + 1) sites, for L 7. The systematic sequence of mean-field solutions confirms the existence of a continuous transition in this system and extrapolations of the critical chemical potential µ2,c(L) and particle density ρ2,c(L) to L → ∞ yield estimates of these quantities in close agreement with previous results for the 2NN model on the square lattice. To confirm the reliability of this approach we employ it also for the 1NN model, where very accurate estimates for the critical parameters µ1,c and ρ1,c -for the fluid-solid transition in this model on the square lattice -are found from extrapolations of data for L 6. The non-classical critical exponents for these transitions are investigated through the coherent anomaly method (CAM), which in the 1NN case yields β and ν differing by at most 6% from the expected Ising exponents. For the 2NN model, the CAM analysis is somewhat inconclusive, because the exponents sensibly depend on the value of µ2,c used to calculate them. Notwithstanding, our results suggest that β and ν are considerably larger than the Ashkin-Teller exponents reported in numerical studies of the 2NN system.

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Polymer models with competing collapse interactions on Husimi and Bethe lattices

Cited by 8 publications

References 50 publications

Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice

Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice

Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares

Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases

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