Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1004.2840 · International Journal of Modern Physics C

ROBUST PARAMETER SELECTION FOR PARALLEL TEMPERING

Firas Hamze, Neil G. Dickson, Kamran Karimi

Published May 1, 2010• 16 citations
arXivHTMLPDF

Abstract

This paper describes an algorithm for selecting parameter values (e.g. temperature values) at which to measure equilibrium properties with Parallel Tempering Monte Carlo simulation. Simple approaches to choosing parameter values can lead to poor equilibration of the simulation, especially for Ising spin systems that undergo first-order phase transitions. However, starting from an initial set of parameter values, the careful, iterative respacing of these values based on results with the previous set of values greatly improves equilibration. Example spin systems presented here appear in the context of Quantum Monte Carlo.

DOI
10.1142/s0129183110015361

Related papers

Efficiency of Parallel Tempering for Ising Systems

Stephan Burkhardt

The efficiency of parallel tempering Monte Carlo is studied for a two-dimensional Ising system of length L with N=L^2 spins. An external field is used to introduce a difference in free energy between the two low temperature states.\nIt is found that the number of replicas R_opt that optimizes the parallel tempering algorithm scales as the square root of the system size N. For two symmetric low temperature states, the time needed for equilibration is observed to grow as L^2.18. If a significant difference in free energy is present between the two states, this changes to L^1.02.\nIt is therefore established that parallel tempering is sped up by a factor of roughly L if an asymmetry is introduced between the low temperature states. This confirms previously made predictions for the efficiency of parallel tempering. These findings should be especially relevant when using parallel tempering for systems like spin glasses, where no information about the degeneracy of low temperature states is available prior to the simulation.

•Aug 15, 2023•0 citations

Parallel-tempering cluster algorithm for computer simulations of critical phenomena

Elmar Bittner, Wolfhard Janke E

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel-tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two orders of magnitude in the performance for two- and three-dimensional Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.

arXiv:1107.5640•Physical Review E•Sep 1, 2011•15 citations

Efficient parallel tempering for first-order phase transitions

T. Neuhaus, Martin P. Magiera, Ulrich H. E. Hansmann

We present a Monte Carlo algorithm that facilitates efficient parallel tempering simulations of the density of states g(E) . We show that the algorithm eliminates the supercritical slowing down in the case of the Q=20 and Q=256 Potts models in two dimensions, typical examples for systems with extreme first-order phase transitions. As recently predicted, and shown here, the microcanonical heat capacity along the calorimetric curve has negative values for finite systems.

Physical Review E•Oct 9, 2007•22 citations

Make life simple: unleash the full power of the parallel tempering algorithm

Elmar Bittner, Andreas Nußbaumer, Wolfhard Janke E

We introduce a new update scheme to systematically improve the efficiency of parallel tempering Monte Carlo simulations by taking into account the temperature dependence of autocorrelation times.In contrast to previous attempts the temperatures are not dynamically adjusted but chosen in such a way that the acceptance rate for proposed exchanges of all adjacent replica is about 50%.We show that by adapting the number of sweeps between the parallel tempering moves to the canonical autocorrelation time, the average round-trip time of a replica between the lowest and the highest temperatures is significantly decreased and, therefore, the efficiency of the parallel tempering algorithm is considerably improved.We illustrate the new algorithm with results for the two-dimensional Ising model and propose a toy model to find the optimal parameter set for the parallel tempering routine within no time.

International Symposium on Lattice Field Theory (LATTICE)•Jun 23, 2010•0 citations

PHASE TRANSITIONS IN SPIN GLASSES

A. P. Young

Some recent progress in Monte Carlo simulations of spin glasses will be presented. The problem of slow dynamics at low temperatures is partially alleviated by use of the parallel tempering (replica exchange) method. A useful technique to check for equilibration (applicable only for a Gaussian distribution) will be discussed. It will be argued that a finite size scaling analysis of the scaled correlation length of the system is a good approach with which to investigate phase transitions in spin glasses. This method will be used to study two questions: (i) whether there is a phase transition in zero field in the Heisenberg spin glass in three dimensions, and (ii) whether there is phase transition in a magnetic field in an Ising spin glass, also in three dimensions.

International Journal of Modern Physics C•Sep 1, 2009•0 citations

Impact of Equilibration Steps on Quantum Monte Carlo for the Spin-1/2 Heisenberg Model

Ali Akbar H. Ali, Mohammad G. Merdan, Hayder M. Abdualjalil

This study delves into the pivotal role of equilibration Monte Carlo steps (𝑖 steps ) in the Stochastic Series Expansion method-a cutting-edge quantum Monte Carlo technique known for its precision in simulating low-dimensional quantum systems.The research focuses on how varying equilibration steps impact the accuracy and stability of ground state energy, sublattice magnetization, specific heat, and susceptibility results, by analyzing the effect of equilibration steps on these physical properties across different temperatures and lattice sizes.Our findings demonstrate that while ground state energy and sublattice magnetization achieve remarkable stability, susceptibility and specific heat present variabilities, especially at low temperatures.Ground state energy stabilizes after approximately 50 equilibration steps.However, excessive equilibration steps lead to unnecessary computational costs without further accuracy improvements.Furthermore, increasing the measurement steps significantly reduces error bars, enhancing reliability, as demonstrated by a 30% reduction in standard deviation with higher counts.Low temperatures exhibit greater variability in specific heat and susceptibility due to complex quantum effects.

Mathematical Modelling and Engineering Problems•Aug 31, 2025•0 citations
This paper describes an algorithm for selecting parameter values (e.g. temperature values) at which to measure equilibrium properties with Parallel Tempering Monte Carlo simulation. Simple approaches to choosing parameter values can lead to poor equilibration of the simulation, especially for Ising spin systems that undergo first-order phase transitions. However, starting from an initial set of parameter values, the careful, iterative respacing of these values based on results with the previous set of values greatly improves equilibration. Example spin systems presented here appear in the context of Quantum Monte Carlo.
The efficiency of parallel tempering Monte Carlo is studied for a two-dimensional Ising system of length L with N=L^2 spins. An external field is used to introduce a difference in free energy between the two low temperature states.\nIt is found that the number of replicas R_opt that optimizes the parallel tempering algorithm scales as the square root of the system size N. For two symmetric low temperature states, the time needed for equilibration is observed to grow as L^2.18. If a significant difference in free energy is present between the two states, this changes to L^1.02.\nIt is therefore established that parallel tempering is sped up by a factor of roughly L if an asymmetry is introduced between the low temperature states. This confirms previously made predictions for the efficiency of parallel tempering. These findings should be especially relevant when using parallel tempering for systems like spin glasses, where no information about the degeneracy of low temperature states is available prior to the simulation.
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel-tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two orders of magnitude in the performance for two- and three-dimensional Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.
We introduce a new update scheme to systematically improve the efficiency of parallel tempering Monte Carlo simulations by taking into account the temperature dependence of autocorrelation times.In contrast to previous attempts the temperatures are not dynamically adjusted but chosen in such a way that the acceptance rate for proposed exchanges of all adjacent replica is about 50%.We show that by adapting the number of sweeps between the parallel tempering moves to the canonical autocorrelation time, the average round-trip time of a replica between the lowest and the highest temperatures is significantly decreased and, therefore, the efficiency of the parallel tempering algorithm is considerably improved.We illustrate the new algorithm with results for the two-dimensional Ising model and propose a toy model to find the optimal parameter set for the parallel tempering routine within no time.
Some recent progress in Monte Carlo simulations of spin glasses will be presented. The problem of slow dynamics at low temperatures is partially alleviated by use of the parallel tempering (replica exchange) method. A useful technique to check for equilibration (applicable only for a Gaussian distribution) will be discussed. It will be argued that a finite size scaling analysis of the scaled correlation length of the system is a good approach with which to investigate phase transitions in spin glasses. This method will be used to study two questions: (i) whether there is a phase transition in zero field in the Heisenberg spin glass in three dimensions, and (ii) whether there is phase transition in a magnetic field in an Ising spin glass, also in three dimensions.
This study delves into the pivotal role of equilibration Monte Carlo steps (𝑖 steps ) in the Stochastic Series Expansion method-a cutting-edge quantum Monte Carlo technique known for its precision in simulating low-dimensional quantum systems.The research focuses on how varying equilibration steps impact the accuracy and stability of ground state energy, sublattice magnetization, specific heat, and susceptibility results, by analyzing the effect of equilibration steps on these physical properties across different temperatures and lattice sizes.Our findings demonstrate that while ground state energy and sublattice magnetization achieve remarkable stability, susceptibility and specific heat present variabilities, especially at low temperatures.Ground state energy stabilizes after approximately 50 equilibration steps.However, excessive equilibration steps lead to unnecessary computational costs without further accuracy improvements.Furthermore, increasing the measurement steps significantly reduces error bars, enhancing reliability, as demonstrated by a 30% reduction in standard deviation with higher counts.Low temperatures exhibit greater variability in specific heat and susceptibility due to complex quantum effects.