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March 27, 20260 citationsOpen Access

Information-Efficiency of Local Observers for Distinguishing 2D Ising and Potts Configurations

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XWXinlei Wang

Key Points

  • The aim is to analyze the efficiency of two observer-count scales when distinguishing configurations in 2D Ising and Potts models.
  • Compared two observer-count scales: adaptive-greedy threshold and information-theoretic birthday-bound threshold.
  • Defined an efficiency ratio to measure observer effectiveness.
  • Investigated three regimes of efficiency across varying temperatures.
  • Identified three efficiency regimes based on temperature: redundant, near-efficient, and complementary observations.
  • Observed a convergence towards efficiency at critical temperature for specific Potts models.
  • Conjectured that efficiency approaches unity at criticality for FK(q) with q values of 2, 3, and 4.

Abstract

We compare two observer-count scales for distinguishing sampled configurations from local observations: an adaptive-greedy threshold and an information-theoretic birthday-bound threshold. Defining the efficiency ratio \ (= K^* ₁₃₀ₘ / K^* ₆ₑ₄₄₃ₘ \), we observe a three-regime pattern across 2D Ising and Potts models: redundant observations (\ (1 \) ) at high temperature. A conditional conjecture under polynomial alpha-mixing suggests \ (1 \) at \ (Tc \) for FK (\ (q \) ) with \ (q \2, 3, 4\ \).

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Cite This Study

Xinlei Wang (2026) studied this question.

synapsesocial.com/papers/69c61f8515a0a509bde17f91https://doi.org/10.5281/zenodo.19222739
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Birthday bound for greedy observer identification at 2D critical points: patch collision entropy controls the log L cost2026
  2. 2Birthday bound for observer convergence: a universal information-budget formula from classical criticality to quantum circuits2026
  3. 3Objectivity as an Information-Theoretic Ratchet: A Framework for Embedded Observers2026
  4. 4Observer thresholds in elementary cellular automata: monotonicity, local degeneracy, and a tripartite classification2026
  5. 5Local nearest-neighbor correlation as a transferable critical indicator: From Ising universality to Binder-blind regimes2026