| 1. |
- Diaz-Mendez, Rogelio, et al.
(författare)
-
Scaling of the magnetic permeability at the Berezinskii–Kosterlitz–Thouless transition from Coulomb gas simulations
- 2018
-
Ingår i: Journal of Statistical Mechanics. - : IOP Publishing. - 1742-5468. ; 2018:12
-
Tidskriftsartikel (refereegranskat)abstract
- A new approach to the Berezinskii–Kosterlitz–Thouless transition in the two-dimensional Coulomb gas model is explored by Monte Carlo simulation and finite size scaling. The usual mapping of a neutral two-dimensional superconductor in zero magnetic field to a Coulomb gas leads to an unscreened logarithmic interaction between the vortices, and with periodic boundary conditions vortex configurations are always vorticity neutral with an equal number of plus and minus vortices. We demonstrate that relaxing the neutrality condition has certain advantages. It leads to non-neutral vortex configurations that can appear in real systems with open boundary conditions and permits calculation of the compressibility, which for thin film superconductors corresponds to the magnetic permeability. The vortex-number fluctuation has remarkable scaling properties at and below the Berezinskii–Kosterlitz–Thouless transition. The fugacity variable becomes dangerously irrelevant in the low-temperature phase and leads to a multiplicative scaling correction to the mean-square vortex-number fluctuation and to the magnetic permeability. This multiplicative correction strongly affects the scaling properties of the vorticity fluctuation at and below the transition. Consequences of these findings are demonstrated using Monte Carlo simulations. Inclusion of the next-higher order correction to scaling is found to play an important role in the analysis of numerical data for the vortex number fluctuation and permits accurate determination of the critical properties.
|
|
| 2. |
- Pigeon, Simon, et al.
(författare)
-
Tracer particle diffusion in a system with hardcore interacting particles
- 2017
-
Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - : IOP Publishing. - 1742-5468. ; 2017:12
-
Tidskriftsartikel (refereegranskat)abstract
- In this study, inspired by the work of Nakazato and Kitahara (1980 Prog. Theor. Phys. 64 2261), we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on a regular Bravais lattice we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.
|
|
| 3. |
- Rosengren, Hjalmar, 1972
(författare)
-
Elliptic pfaffians and solvable lattice models
- 2016
-
Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - : IOP Publishing. - 1742-5468. ; 2016:8
-
Tidskriftsartikel (refereegranskat)abstract
- We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.
|
|
| 4. |
- Bo, Stefano, et al.
(författare)
-
Functionals in stochastic thermodynamics : how to interpret stochastic integrals
- 2019
-
Ingår i: Journal of Statistical Mechanics. - : IOP Publishing. - 1742-5468.
-
Tidskriftsartikel (refereegranskat)abstract
- In stochastic thermodynamics standard concepts from macroscopic thermodynamics, such as heat, work, and entropy production, are generalized to small fluctuating systems by defining them on a trajectory-wise level. In Langevin systems with continuous state-space such definitions involve stochastic integrals along system trajectories, whose specific values depend on the discretization rule used to evaluate them (i.e. the 'interpretation' of the noise terms in the integral). Via a systematic mathematical investigation of this apparent dilemma, we corroborate the widely used standard interpretation of heat-and work-like functionals as Stratonovich integrals. We furthermore recapitulate the anomalies that are known to occur for entropy production in the presence of temperature gradients.
|
|
| 5. |
|
|
| 6. |
- Del Ferraro, Gino, 1983-, et al.
(författare)
-
On one-step replica symmetry breaking in the Edwards-Anderson spin glass model
- 2016
-
Ingår i: Journal of statistical physics. - : Institute of Physics (IOP). - 0022-4715 .- 1572-9613.
-
Tidskriftsartikel (refereegranskat)abstract
- We consider a one-step replica symmetry breaking description of the Edwards–Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a generalized belief propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter y, and that the Kikuchi approximation of this generalized free energy leads to second-level, one-step replica symmetry breaking (1RSB), GBP equations. We then proceed analogously to the Bethe approximation case for tree-like graphs, where it has been shown that 1RSB belief propagation equations admit a survey propagation solution. We discuss when and how the one-step-replica symmetry breaking GBP equations that we obtain also allow a simpler class of solutions which can be interpreted as a class of generalized survey propagation equations for the single instance graph case.
|
|
| 7. |
- Dominguez Vazquez, Eduardo, et al.
(författare)
-
A simple analytical description of the non-stationary dynamics in Ising spin systems
- 2017
-
Ingår i: Journal of Statistical Mechanics. - : IOP PUBLISHING LTD. - 1742-5468.
-
Tidskriftsartikel (refereegranskat)abstract
- The analytical description of the dynamics in models with discrete variables (e.g. Ising spins) is a notoriously di. cult problem, which can only be tackled under some approximation. Recently a novel variational approach to solve the stationary dynamical regime has been introduced by Pelizzola ( 2013 Eur. Phys. J. B 86 120), where simple closed equations are derived under meanfield approximations based on the cluster variational method. Here we propose to use the same approximation based on the cluster variational method also for the non- stationary regime, which has not been considered up to now within this framework. We check the validity of this approximation in describing the nonstationary dynamical regime of several Ising models defined on Erdos-Renyi random graphs: we study ferromagnetic models with symmetric and partially asymmetric couplings, models with random fields and also spin glass models. A comparison with the actual Glauber dynamics, solved numerically, shows that pone of the two studied approximations (the so-called `diamond' approximation) provides very accurate results in all the systems studied. Only for the spin glass models do we find some small discrepancies in the very low temperature phase, probably due to the existence of a large number of metastable states. Given the simplicity of the equations to be solved, we believe the diamond approximation should be considered as the `minimal standard' in the description of the nonstationary regime of Ising-like models: any new method pretending to provide a better approximate description to the dynamics of Ising-like models should perform at least as good as the diamond approximation.
|
|
| 8. |
- Kjäll, Jonas, et al.
(författare)
-
Matrix product state representation of quasielectron wave functions
- 2018
-
Ingår i: Journal of Statistical Mechanics-Theory and Experiment. - : IOP Publishing. - 1742-5468.
-
Tidskriftsartikel (refereegranskat)abstract
- Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.
|
|
| 9. |
- Matern, S., et al.
(författare)
-
Entanglement in 3D Kitaev spin liquids
- 2018
-
Ingår i: Journal of Statistical Mechanics-Theory and Experiment. - : IOP Publishing. - 1742-5468.
-
Tidskriftsartikel (refereegranskat)abstract
- Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids axe the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures-ranging from topologically protected Weyl semimetals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.
|
|
| 10. |
- Battistin, Claudia, et al.
(författare)
-
Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins
- 2015
-
Ingår i: Journal of Statistical Mechanics. - 1742-5468.
-
Tidskriftsartikel (refereegranskat)abstract
- We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief propagation (BP) and susceptibility propagation (SusP) can then be used to infer the states of hidden variables and to learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the Thouless-Anderson-Palmer (TAP) equations for reconstructing the connections.
|
|
