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Linear relaxation in large two-dimensional Ising models.

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  • 1Department of Physics, Xiamen University, Xiamen, Fujian 361005, China.

Physical Review. E
|March 18, 2016
PubMed
Summary
This summary is machine-generated.

Simulations of critical dynamics in large Ising lattices reveal dynamic scaling laws. This research on field-programmable gate-array computing advances understanding of critical phenomena in two-dimensional systems.

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Area of Science:

  • Statistical physics
  • Computational physics

Background:

  • The Ising model is a fundamental model in statistical mechanics used to study phase transitions.
  • Understanding critical dynamics is crucial for characterizing systems near critical points.

Purpose of the Study:

  • To simulate critical dynamics in large two-dimensional Ising lattices (up to 2048x2048).
  • To measure linear relaxation times and verify dynamic scaling laws.
  • To determine the dynamic exponent z for these systems.

Main Methods:

  • Simulations performed on field-programmable-gate-array (FPGA)-based computing devices.
  • Extremely long Monte Carlo simulations were conducted, with the longest involving 7.1x10^16 spin updates.
  • Linear relaxation times were measured to analyze critical dynamics.

Main Results:

  • Linear relaxation times follow the dynamic scaling law for correlation lengths up to 2048.
  • The dynamic exponent z was found to be 2.179(12), consistent with prior studies.
  • Simulations of Ising lattices larger than 512x512 are highly sensitive to pseudorandom number correlations.

Conclusions:

  • The study confirms dynamic scaling laws in large 2D Ising lattices.
  • The findings provide accurate measurement of the dynamic exponent z.
  • Challenges in simulating large systems due to pseudorandom number sensitivity were identified.