| 1. |
- Keesman, Rick, et al.
(författare)
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Finite-size scaling at infinite-order phase transitions
- 2016
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - : IOP Publishing. - 1742-5468. ; 2016:9, s. 093201-
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Tidskriftsartikel (refereegranskat)abstract
- For systems with infinite-order phase transitions, in which an order parameter smoothly becomes nonzero, a new observable for finite-size scaling analysis is suggested. By construction this new observable has the favourable property of diverging at the critical point. Focussing on the example of the F-model we compare the analysis of this observable with that of another observable, which is also derived from the order parameter but does not diverge, as well as that of the associated susceptibility. We discuss the difficulties that arise in the finite-size scaling analysis of such systems. In particular we show that one may reach incorrect conclusions from large-system size extrapolations of observables that are not known to diverge at the critical point. Our work suggests that one should base finite-size scaling analyses for infinite-order phase transitions only on observables that are guaranteed to diverge.
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| 2. |
- Keesman, Rick, et al.
(författare)
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Numerical study of the F model with domain-wall boundaries
- 2017
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Ingår i: Physical Review E. - 2470-0045 .- 2470-0053. ; 95:5
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Tidskriftsartikel (refereegranskat)abstract
- We perform a numerical study of the F model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size as well as its asymptotics and leading finite-size corrections. To complement this picture we use a full lattice multicluster algorithm to study equilibrium properties of this model for systems of moderate size, up to L=512. We compare the energy to its exactly known large-L asymptotics. We investigate the model's infinite-order phase transition by means of finite-size scaling for an observable derived from the staggered polarization in order to test the method put forward in our recent joint work with Duine and Barkema. In addition we analyze local properties of the model. Our data are perfectly consistent with analytical expressions for the arctic curves. We investigate the structure inside the temperate region of the lattice, confirming the oscillations in vertex densities that were first observed by Syljuåsen and Zvonarev and recently studied by Lyberg et al. We point out "(anti)ferroelectric" oscillations close to the corresponding frozen regions as well as "higher-order" oscillations forming an intricate pattern with saddle-point-like features.
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| 3. |
- Lamers, Jules, 1986
(författare)
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Resurrecting the partially isotropic Haldane-Shastry model
- 2018
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 97
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Tidskriftsartikel (refereegranskat)abstract
- © 2018 American Physical Society. We present an alternative, simpler expression for the Hamiltonian of the partially isotropic (XXZ-like) version of the Haldane-Shastry model, which was derived by D. Uglov over two decades ago in an apparently little-known preprint. While resembling the pairwise long-range form of the Haldane-Shastry model, our formula accounts for the multispin interactions obtained by Uglov. Our expression is physically meaningful, makes hermiticity manifest, and is computationally more efficient. We discuss the model's properties, including its limits and (ordinary and quantum-affine) symmetries, and review the model's exact spectrum found by Uglov for finite spin-chain length, which parallels the isotropic case up to level splitting due to the anisotropy. We also extend the partially isotropic model to higher rank, with SU(n) "spins," for which the spectrum is determined by sln motifs.
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| 4. |
- Lamers, Jules, 1986
(författare)
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The Functional Method for the Domain-Wall Partition Function
- 2018
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Ingår i: Symmetry Integrability and Geometry-Methods and Applications. - : SIGMA (Symmetry, Integrability and Geometry: Methods and Application). - 1815-0659. ; 14
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Tidskriftsartikel (refereegranskat)abstract
- We review the (algebraic-)functional method devised by Galleas and further developed by Galleas and the author. We first explain the method using the simplest example: the computation of the partition function for the six-vertex model with domain-wall boundary conditions. At the heart of the method lies a linear functional equation for the partition function. After deriving this equation we outline its analysis. The result is a closed expression in the form of a symmetrized sum - or, equivalently, multiple-integral formula - that can be rewritten to recover Izergin's determinant. Special attention is paid to the relation with other approaches. In particular we show that the Korepin-Izergin approach can be recovered within the functional method. We comment on the functional method's range of applicability, and review how it is adapted to the technically more involved example of the elliptic solid-on-solid model with domain walls and a reflecting end. We present a new formula for the partition function of the latter, which was expressed as a determinant by Tsuchiya-Filali-Kitanine. Our result takes the form of a 'crossing-symmetrized' sum with 2(L) terms featuring the elliptic domain-wall partition function, which appears to be new also in the limiting case of the six-vertex model. Further taking the rational limit we recover the expression obtained by Frassek using the boundary perimeter Bethe ansatz.
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| 5. |
- Lamers, Jules, 1986
(författare)
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The Functional Method for the Domain-Wall Partition Function
- 2018
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Ingår i: Symmetry, Integrability and Geometry - Methods and Applications. - 1815-0659. ; 14
-
Forskningsöversikt (refereegranskat)abstract
- We review the (algebraic-)functional method devised by Galleas and further developed by Galleas and the author. We first explain the method using the simplest example: the computation of the partition function for the six-vertex model with domain-wall boundary conditions. At the heart of the method lies a linear functional equation for the partition function. After deriving this equation we outline its analysis. The result is a closed expression in the form of a symmetrized sum - or, equivalently, multiple-integral formula - that can be rewritten to recover Izergin's determinant. Special attention is paid to the relation with other approaches. In particular we show that the Korepin-Izergin approach can be recovered within the functional method. We comment on the functional method's range of applicability, and review how it is adapted to the technically more involved example of the elliptic solid-on-solid model with domain walls and a reflecting end. We present a new formula for the partition function of the latter, which was expressed as a determinant by Tsuchiya-Filali-Kitanine. Our result takes the form of a 'crossing-symmetrized' sum with 2(L) terms featuring the elliptic domain-wall partition function, which appears to be new also in the limiting case of the six-vertex model. Further taking the rational limit we recover the expression obtained by Frassek using the boundary perimeter Bethe ansatz.
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