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Area of Science:

  • * Theoretical physics
  • * Statistical mechanics
  • * Quantum field theory

Background:

  • * Conformal field theories (CFTs) describe critical phenomena.
  • * Calculating thermodynamic properties like free-energy density is challenging.
  • * Finite temperature effects require specialized theoretical treatment.

Purpose of the Study:

  • * To introduce a novel numerical method for estimating one-point functions and free-energy density in CFTs at finite temperature.
  • * To validate the method by applying it to the critical O(N) model.

Main Methods:

  • * Solving the Kubo-Martin-Schwinger (KMS) condition numerically.
  • * Analyzing two-point functions of identical scalars.
  • * Applying the method to the critical O(N) model for N=1, 2, 3 in dimensions 3 ≤ d ≤ 4.

Main Results:

  • * Successful estimation of one-point functions and free-energy density.
  • * Agreement with established Monte Carlo simulation results for the 3D Ising model (N=1).
  • * New predictions for the critical O(N) model with N=2 and N=3.

Conclusions:

  • * The proposed numerical method is effective for studying CFTs at finite temperatures.
  • * The method provides a viable alternative to computationally intensive simulations.
  • * The results offer valuable insights into the behavior of critical systems.