# Universality and scaling laws in the cascading failure model with healing

## TL;DR

This paper investigates the scaling laws and universality classes in a cascading failure model with healing, revealing how the transition behavior changes with the healing parameter and identifying two distinct universality classes.

## Contribution

It introduces a detailed analysis of the scaling behavior and universality classes in a healing cascading failure model, extending previous work on hybrid phase transitions.

## Key findings

- Two universality classes identified based on the healing parameter
- Exponents match the original model below the critical healing value
- Above the critical healing, the model exhibits trivial scaling with Gaussian fluctuations

## Abstract

Cascading failures may lead to dramatic collapse in interdependent networks, where the breakdown takes place as a discontinuity of the order parameter. In the cascading failure (CF) model with healing there is a control parameter which at some value suppresses the discontinuity of the order parameter. However, up to this value of the healing parameter the breakdown is a hybrid transition, meaning that, besides this first order character, the transition shows scaling too. In this paper we investigate the question of universality related to the scaling behavior. Recently we showed that the hybrid phase transition in the original CF model has two sets of exponents describing respectively the order parameter and the cascade statistics, which are connected by a scaling law. In the CF model with healing we measure these exponents as a function of the healing parameter. We find two universality classes: In the wide range below the critical healing value the exponents agree with those of the original model, while above this value the model displays trivial scaling meaning that fluctuations follow the central limit theorem.