Pith Number

pith:C4BLUMPH

pith:2026:C4BLUMPHPNRFPZKF4HKJAZ2HAC

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Energy-Weighted Site Percolation in Two Dimensions

Kabir Ramola, Sayan Sircar

Bond energy shifts the percolation threshold smoothly and changes the correlation-length exponent continuously in two dimensions.

arxiv:2605.18312 v1 · 2026-05-18 · cond-mat.stat-mech · cond-mat.dis-nn

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Claims

C1strongest claim

Using Monte Carlo simulations and real-space renormalization-group (RG) methods, we show that bond energy shifts the percolation threshold smoothly. We define an energy-weighted correlation length that remains finite at the classical site occupation threshold (p_c(ε=0)) and shrinks with increasing ε, capturing the energetic suppression of large-scale connectivity.

C2weakest assumption

The real-space RG with Kadanoff block recursions accurately tracks the continuous evolution of the correlation-length exponent ν from 1/2 to 4/3 to 1 and matches Coulomb-gas predictions for loop models without requiring additional parameters or post-hoc adjustments specific to the energy term.

C3one line summary

Adding a continuous bond energy ε to 2D site percolation shifts the threshold smoothly and drives the correlation-length exponent ν from 1/2 through 4/3 to 1, as shown by Monte Carlo simulations and real-space RG that also reveal an energy-weighted correlation length and antiferromagnetic ordering,

References

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[1] In the dense cluster limit, asεapproaches−∞, loops become abundant with a loop fugacity ofn= 2

[2] D. Stauffer and A. Aharony,Introduction to Percolation Theory(Taylor & Francis, 1994) 1994

[3] Bollob´ as and O 2006

[4] Kesten,Percolation Theory for Mathematicians (Birkh¨ auser, 1982) 1982

[5] Sahimi,Applications of Percolation Theory(Taylor & Francis, 1994) 1994

Formal links

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Receipt and verification

First computed	2026-05-20T00:05:54.552113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1702ba31e77b6257e545e1d4906747008034e37ba8889b25e4ca19c90df36536

Aliases

arxiv: 2605.18312 · arxiv_version: 2605.18312v1 · doi: 10.48550/arxiv.2605.18312 · pith_short_12: C4BLUMPHPNRF · pith_short_16: C4BLUMPHPNRFPZKF · pith_short_8: C4BLUMPH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/C4BLUMPHPNRFPZKF4HKJAZ2HAC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 1702ba31e77b6257e545e1d4906747008034e37ba8889b25e4ca19c90df36536

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d76627c954c44d41b7599c00c4468051ed2233d1fa58956eaf174378b51363a",
    "cross_cats_sorted": [
      "cond-mat.dis-nn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-18T12:30:51Z",
    "title_canon_sha256": "66d0abc3c176b044f2e36524e9b7c2c2f6ce18e154a1b23fba504e3324012bac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18312",
    "kind": "arxiv",
    "version": 1
  }
}