Efficient method of finding scaling exponents from finite-size Monte-Carlo simulations

Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique of dealing the problem of finite-size scaling. The efficiency of the technique is demonstrated on two data sets.

💡 Research Summary

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The paper addresses a persistent problem in Monte‑Carlo studies of critical phenomena: finite‑size effects often obscure the true scaling exponents, making extrapolation to the thermodynamic limit unreliable. Traditional approaches rely on plotting observable L versus system size N on a log‑log scale, identifying a linear regime, and extracting the slope as the exponent α. This works only when finite‑size corrections are small or decay rapidly; otherwise the linear region may be absent or ambiguous, and the uncertainty of the exponent becomes large.

The authors propose a fundamentally different strategy that exploits the existence of several observables Lₖ(N) (k = 1,…,m) that share the same leading scaling exponent α₁. Assuming each observable admits an asymptotic expansion

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