Publications by authors named "Gert Aarts"

6 Publications

  • Page 1 of 1

Mapping distinct phase transitions to a neural network.

Phys Rev E 2020 Nov;102(5-1):053306

Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, Swansea, Wales, United Kingdom.

We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems irrespective of the universality class, order, and the presence of discrete or continuous degrees of freedom. No prior knowledge about the existence of a phase transition is required in the target system and its entire parameter space can be scanned with multiple histogram reweighting to discover one. We establish our approach in q-state Potts models and perform a calculation for the critical coupling and the critical exponents of the ϕ^{4} scalar field theory using quantities derived from the neural network implementation. We view the machine learning algorithm as a mapping that associates each configuration across different systems to its corresponding phase and elaborate on implications for the discovery of unknown phase transitions.
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http://dx.doi.org/10.1103/PhysRevE.102.053306DOI Listing
November 2020

Extending machine learning classification capabilities with histogram reweighting.

Phys Rev E 2020 Sep;102(3-1):033303

Department of Mathematics, Swansea University, Bay Campus, SA1 8EN, Swansea, Wales, United Kingdom.

We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. In our approach, we treat the output from a convolutional neural network as an observable in a statistical system, enabling its extrapolation over continuous ranges in parameter space. We demonstrate our proposal using the phase transition in the two-dimensional Ising model. By interpreting the output of the neural network as an order parameter, we explore connections with known observables in the system and investigate its scaling behavior. A finite-size scaling analysis is conducted based on quantities derived from the neural network that yields accurate estimates for the critical exponents and the critical temperature. The method improves the prospects of acquiring precision measurements from machine learning in physical systems without an order parameter and those where direct sampling in regions of parameter space might not be possible.
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http://dx.doi.org/10.1103/PhysRevE.102.033303DOI Listing
September 2020

Electrical conductivity of the quark-gluon plasma across the deconfinement transition.

Phys Rev Lett 2013 Oct 23;111(17):172001. Epub 2013 Oct 23.

Department of Physics, College of Science, Swansea University, Swansea SA2 8PP, United Kingdom and Institute for Theoretical Physics, Universität Regensburg, D-93040 Regensburg, Germany.

A lattice calculation is presented for the electrical conductivity σ of the QCD plasma with 2+1 dynamical flavors at nonzero temperature. We employ the conserved lattice current on anisotropic lattices using a tadpole-improved clover action and study the behavior of the conductivity over a wide range of temperatures, both below and above the deconfining transition. The conductivity is extracted from a spectral-function analysis using the maximal entropy method, and a discussion of its systematics is provided. We find an increase of σ/T across the transition.
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http://dx.doi.org/10.1103/PhysRevLett.111.172001DOI Listing
October 2013

Can stochastic quantization evade the sign problem? The relativistic bose gas at finite chemical potential.

Authors:
Gert Aarts

Phys Rev Lett 2009 Apr 1;102(13):131601. Epub 2009 Apr 1.

Department of Physics, Swansea University, Swansea SA2 8PP, United Kingdom.

A nonperturbative study of field theories with a complex action, such as QCD at finite baryon density, is difficult due to the sign problem. We show that the relativistic Bose gas at finite chemical potential has a sign and "silver blaze" problem, similar to QCD. We then apply stochastic quantization and complex Langevin dynamics to study this theory with nonperturbative lattice simulations. Independence of chemical potential at small and a transition to a condensed phase at large chemical potential are found. Lattices of size N4, with N=4, 6, 8, 10, are used. We show that the sign problem is severe, however, we find that it has no negative effect using this approach. This improves the prospects of applying stochastic quantization to QCD at nonzero density.
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http://dx.doi.org/10.1103/PhysRevLett.102.131601DOI Listing
April 2009

Spectral functions at small energies and the electrical conductivity in hot quenched lattice QCD.

Phys Rev Lett 2007 Jul 13;99(2):022002. Epub 2007 Jul 13.

Department of Physics, Swansea University, Swansea SA2 8PP, United Kingdom.

In lattice QCD, the maximum entropy method can be used to reconstruct spectral functions from Euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and gives a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.
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http://dx.doi.org/10.1103/PhysRevLett.99.022002DOI Listing
July 2007

Classical aspects of quantum fields far from equilibrium.

Phys Rev Lett 2002 Jan 15;88(4):041603. Epub 2002 Jan 15.

Institut für Theoretische Physik, Philosophenweg 16, 69120 Heidelberg, Germany.

We consider the time evolution of nonequilibrium quantum scalar fields in the O(N) model, using the next-to-leading order 1/N expansion of the two-particle irreducible effective action. A comparison with exact numerical simulations in 1+1 dimensions in the classical limit shows that the 1/N expansion gives quantitatively precise results already for moderate values of N. For sufficiently high initial occupation numbers the time evolution of quantum fields is shown to be accurately described by classical physics. Eventually the correspondence breaks down due to the difference between classical and quantum thermal equilibrium.
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http://dx.doi.org/10.1103/PhysRevLett.88.041603DOI Listing
January 2002
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