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High-precision thermodynamic and critical properties from tensor renormalization-group flows.

Michael Hinczewski1, A Nihat Berker

  • 1Feza Gürsey Research Institute, TUBITAK-Bosphorus University, Cengelköy 34684, Istanbul, Turkey.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary

The new tensor renormalization-group (TRG) method precisely calculates critical properties for lattice models. This advanced technique offers systematic improvements for analyzing phase diagrams and thermodynamic functions.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • The tensor renormalization-group (TRG) method is a recent advancement for analyzing lattice Hamiltonians.
  • TRG utilizes local coarse-graining transformations of tensors to represent interactions undergoing renormalization-group flows.

Purpose of the Study:

  • To precisely derive thermodynamic and critical properties of lattice Hamiltonians.
  • To establish a connection between tensor flows and the phase diagram structure of infinite systems.
  • To calculate critical exponents and thermodynamic functions across the entire temperature range.

Main Methods:

  • Applying the TRG method as a local coarse-graining transformation.
  • Analyzing tensor flows to understand phase diagram structure and identify fixed points.
  • Utilizing fixed-point analysis and summation along flows to determine critical exponents and thermodynamic functions.

Main Results:

  • The TRG method accurately calculates thermodynamic and critical properties.
  • Free energy for the ferromagnetic triangular lattice Ising model was computed with precision better than 10(-5) over the entire temperature range.
  • The method demonstrates systematic convergence and straightforward improvements with increasing tensor index range (D).

Conclusions:

  • The TRG method provides a highly precise and systematic approach for studying lattice Hamiltonians.
  • It offers a powerful tool for exploring phase diagrams and calculating thermodynamic properties.
  • The method shows significant advantages over previous position-space renormalization-group techniques.