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Berezinskii-Kosterlitz-Thouless transition in a context-sensitive random language model.

Yuma Toji1, Jun Takahashi2, Vwani Roychowdhury3

  • 1Hokkaido University, Graduate School of Information Science and Technology, Sapporo, Hokkaido 060-0814, Japan.

Physical Review. E
|February 20, 2026
PubMed
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Researchers demonstrate a phase transition in a novel language model, inspired by physics. This finding suggests natural language critical properties may stem from Berezinskii-Kosterlitz-Thouless (BKT) phases, not just fine-tuning.

Area of Science:

  • Statistical Physics
  • Computational Linguistics
  • Natural Language Processing

Background:

  • Power-law critical properties in natural languages resemble physical systems' phase transitions.
  • Large language models (LLMs) show similarities to physics concepts like scaling laws.
  • A gap exists in identifying generative language models exhibiting statistical physics-defined phase transitions.

Purpose of the Study:

  • To construct and analyze a probabilistic language model exhibiting a phase transition.
  • To investigate the applicability of statistical physics concepts to natural language modeling.
  • To explore the nature of critical properties in natural languages.

Main Methods:

  • Developed a context-sensitive random language model inspired by the 1D Potts model.

Related Experiment Videos

  • Numerically demonstrated an unambiguous phase transition by tuning a model parameter.
  • Defined and analyzed an order parameter capturing symbol frequency biases.

    • Main Results:

    • The order parameter transitioned from zero to non-zero in the infinite-length limit, indicating a singularity.
    • Identified the transition as a variant of the Berezinskii-Kosterlitz-Thouless (BKT) transition.
    • Observed BKT phase characteristics in a one-dimensional system, a rare phenomenon.

    Conclusions:

    • Natural language critical properties might be generically explained by BKT phases.
    • This challenges the need for fine-tuning or self-organized criticality to explain language properties.
    • The study provides a rare example of a BKT phase in a 1D system, with implications for physics and linguistics.