The LR-SR bridge equivalence and quantitative Sak predictions for percolation

Key Points

• This research aims to demonstrate the equivalence of long-range percolation exponents and the bridge identity across all dimensions.
• Proved algebraic identities related to long-range percolation exponents.
• Developed theoretical propositions to support the findings.
• Presented three theorems validating the results.
• Established that Hutchcroft's long-range percolation exponents are algebraically identical to the bridge identity.
• Validated the results across all dimensions, strengthening the theoretical framework for percolation.
• Contributed to the larger Universal program related to critical phenomena.