# Slip-Size Distribution and Self-Organized Criticality in Block-Spring Models with Quenched Randomness

## TL;DR

This paper investigates slip-size distributions and self-organized criticality in block-spring models with quenched randomness, revealing power-law slip distributions and phase transitions influenced by different friction laws.

## Contribution

It introduces analysis of slip-size distributions in block-spring models with quenched randomness, highlighting self-organized criticality and phase transitions under various friction conditions.

## Key findings

- Slip-size distributions follow power laws with exponents similar to the quenched Edwards-Wilkinson model.
- Self-organized critical states emerge under slow external force increase.
- Phase transitions occur in models with velocity-strengthening friction.

## Abstract

We study slowly pulling block-spring models in random media. Second-order phase transitions exist in a model pulled by a constant force in the case of velocity-strengthening friction. If external forces are slowly increased, nearly critical states are self-organized. Slips of various sizes occur, and the probability distributions of slip size roughly obey power laws. The exponent is close to that in the quenched Edwards--Wilkinson model. Furthermore, the slip-size distributions are investigated in cases of Coulomb friction, velocity-weakening friction.