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Phase transitions in Edwards–Anderson model by means of information theory

Author

Listed:
  • Vogel, E.E.
  • Saravia, G.
  • Bachmann, F.
  • Fierro, B.
  • Fischer, Janine

Abstract

A numeric method to characterize phase transitions is presented, explained and applied to a two-dimensional disordered system that can be thought of as a diluted ferromagnet or an Edwards–Anderson model near the ferromagnetic limit. A computer simulation is implemented to define a time series for order parameters; a file stores the time evolution of each parameter for different dilution concentrations and for a series of temperatures. These files are compressed and they reach a maximum size for temperatures in agreement with critical temperatures for the ferromagnetic/paramagnetic transition obtained by other methods. Site order parameter gives optimum results for this method based on data compression. Data compression procedures are invoked to give a qualitative explanation of this phenomenon. The advantages of this method are discussed by comparing results and procedures with two established methods: the crossing of Binder cumulants and the crossing of time autocorrelation functions. Other possible applications and extensions of this method are also mentioned.

Suggested Citation

  • Vogel, E.E. & Saravia, G. & Bachmann, F. & Fierro, B. & Fischer, Janine, 2009. "Phase transitions in Edwards–Anderson model by means of information theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4075-4082.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:19:p:4075-4082
    DOI: 10.1016/j.physa.2009.06.010
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    Cited by:

    1. Vogel, E.E. & Saravia, G. & Kobe, S. & Schumann, R. & Schuster, R., 2018. "A novel method to optimize electricity generation from wind energy," Renewable Energy, Elsevier, vol. 126(C), pages 724-735.
    2. Vogel, E.E. & Saravia, G. & Cortez, L.V., 2012. "Data compressor designed to improve recognition of magnetic phases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1591-1601.
    3. Pasten, Denisse & Saravia, Gonzalo & Vogel, Eugenio E. & Posadas, Antonio, 2022. "Information theory and earthquakes: Depth propagation seismicity in northern Chile," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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