Exact finite-size corrections and corner free energies for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math> universality class

Измаилян, Н. Ш.; Kenna, Ralph; Guo, Wenan; Wu, Xintian

doi:10.1016/j.nuclphysb.2014.04.023

Cited by 9 publications

(20 citation statements)

References 39 publications

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“…Later the conformal field theory prediction Eq. (6) was confirmed [7] for the dimer model on odd-odd square lattices with one monomer on the boundary, for which the central charge is c = −2. However, for another model in the c = −2 universality class, namely the spanning-tree model, Duplantier and David [17] found logarithmic correction terms in the free energy for periodic and free-boundary conditions, which appeared to contradict the conformal field theory prediction.…”

Section: Introductionmentioning

confidence: 79%

“…The general theory for the asymptotic expansion of Z 0,0 (z,M,N) has been given in Ref. [7] and the asymptotic expansion of Z α,β (z,M,N) for (α,β) = (0,0) has been given in Refs. [3,5].…”

Section: Partition Function With Twisted Boundary Conditionmentioning

confidence: 99%

“…In the quest to improve our understanding of realistic systems of finite extent, two-dimensional models play crucial roles in statistical mechanics as they have long served as a testing ground to explore the general ideas of finite-size scaling under controlled conditions. Of particular importance in such studies are exact results where the analysis can be carried out without numerical errors, the Ising model [1][2][3], the dimer, and spanning tree model [4][5][6][7] being the most prominent examples.…”

Section: Introductionmentioning

confidence: 99%

“…They found that the aspect-ratio dependence of finite-size corrections is sensitive to boundary conditions and the parity of the number of lattice sites along the lattice axis. Quite recently, Izmailian et al [7] have found that the partition functions of the anisotropic dimer model on the rectangular (2M − 1) × (2N − 1) lattice with free and cylindrical-boundary conditions with a single monomer residing on the boundary can be expressed in terms of a partition function with twisted-boundary conditions Z α,β with * ab5223@coventry.ac.uk; izmail@yerphi.am † r.kenna@coventry.ac.uk (α,β) = (0,0). Based on these expressions, they derive the exact asymptotic expansions of the free energy.…”

Section: Introductionmentioning

confidence: 99%

“…Our objective in this paper is to study the finite-size properties of a spanning tree on the plane square lattice under five different sets of boundary conditions using the same techniques developed in Refs. [3,5] and [7]. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Exact finite-size corrections for the spanning-tree model under different boundary conditions

Измаилян

Kenna

2015

Phys. Rev. E

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CURVE is the Institutional Repository for Coventry UniversityWe express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.

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Section: Introductionmentioning

confidence: 79%

Section: Partition Function With Twisted Boundary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Exact finite-size corrections for the spanning-tree model under different boundary conditions

Измаилян

Kenna

2015

Phys. Rev. E

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Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics

Allegra

2015

Nuclear Physics B

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International audienceIn this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model via the so-called height mapping and the nature of boundary conditions is unravelled. The complete and detailed fermionic solution of the dimer model on the square lattice with an arbitrary number of monomers is presented, and finite size effect analysis is performed to study surface and corner effects, leading to the extrapolation of the central charge of the model. The solution allows for exact calculations of monomer and dimer correlation functions in the discrete level and the scaling behavior can be inferred in order to find the set of scaling dimensions and compare to the bosonic theory which predicts particular features concerning corner behaviors. Finally, some combinatorial and numerical properties of partition functions with boundary monomers are discussed, proved and checked with enumeration algorithms

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Integrability and conformal data of the dimer model

Morin-Duchesne

Rasmussen

Ruelle

2016

J. Phys. A: Math. Theor.

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The central charge of the dimer model on the square lattice is still being debated in the literature. In this paper, we provide evidence supporting the consistency of a c = −2 description. Using Lieb's transfer matrix and its description in terms of the Temperley-Lieb algebra TL n at β = 0, we provide a new solution of the dimer model in terms of the model of critical dense polymers on a tilted lattice and offer an understanding of the lattice integrability of the dimer model. The dimer transfer matrix is analysed in the scaling limit and the result for L 0 − c 24 is expressed in terms of fermions. Higher Virasoro modes are likewise constructed as limits of elements of TL n and are found to yield a c = −2 realisation of the Virasoro algebra, familiar from fermionic bc ghost systems. In this realisation, the dimer Fock spaces are shown to decompose, as Virasoro modules, into direct sums of Feigin-Fuchs modules, themselves exhibiting reducible yet indecomposable structures. In the scaling limit, the eigenvalues of the lattice integrals of motion are found to agree exactly with those of the c = −2 conformal integrals of motion. Consistent with the expression for L 0 − c 24 obtained from the transfer matrix, we also construct higher Virasoro modes with c = 1 and find that the dimer Fock space is completely reducible under their action. However, the transfer matrix is found not to be a generating function for the c = 1 integrals of motion. Although this indicates that Lieb's transfer matrix description is incompatible with the c = 1 interpretation, it does not rule out the existence of an alternative, c = 1 compatible, transfer matrix description of the dimer model.

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Exact finite-size corrections and corner free energies for the c=−2 universality class

Cited by 9 publications

References 39 publications

Exact finite-size corrections for the spanning-tree model under different boundary conditions

Exact finite-size corrections for the spanning-tree model under different boundary conditions

Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics

Integrability and conformal data of the dimer model

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