Conformable Scaling and Critical Dynamics: A Unified Framework for Phase Transitions

TL;DR

This paper introduces a conformable derivative framework to model critical phenomena in phase transitions, providing unified expressions for thermodynamic quantities and successfully fitting experimental data, bridging classical and generalized scaling theories.

Contribution

It develops a novel conformable derivative approach to describe critical dynamics, integrating scale invariance and critical slowing down without fractional calculus, and applies it to superconducting transitions.

Findings

Analytical expressions for thermodynamic observables near criticality.

Excellent fit of the model to niobium experimental data.

Captures asymmetric scaling behavior around Tc.

Abstract

We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for thermodynamic observables such as heat capacity, magnetization, susceptibility, and coherence length, each exhibiting power-law behavior near the critical temperature. The conformable derivative framework naturally embeds scale invariance and critical slowing down into the dynamics without resorting to fully nonlocal fractional calculus. Modified Ginzburg-Landau equations are constructed to model superconducting transitions, leading to analytical expressions for the order parameter and London penetration depth. Experimental data from niobium confirm the model's applicability, showing excellent fits and capturing asymmetric scaling behavior around Tc. This work offers a bridge between classical mean-field theory and generalized scaling frameworks, with implications for both theoretical modeling and experimental analysis.