# Static approach to renormalization group analysis of stochastic models with spatially quenched disorder

## TL;DR

This paper introduces a static renormalization group method for stochastic surface models with quenched disorder, revealing shifts in critical dimensions and deriving critical exponents for various models.

## Contribution

It proposes a novel static RG approach involving only time-independent quantities for quenched stochastic models, expanding analysis capabilities.

## Key findings

- Upper critical dimension shifts by two units in quenched models
- Derived critical exponents and scaling regimes for studied models
- Obtained some exact critical exponent values and relations

## Abstract

A new ''static'' renormalization group approach to stochastic models of fluctuating surfaces with spatially quenched noise is proposed in which only time-independent quantities are involved. As examples, quenched versions of the Kardar-Parisi-Zhang model and its Pavlik's modification, the Hwa-Kardar model of self-organized criticality, and Pastor-Satorras-Rothman model of landscape erosion are studied. It is shown that the upper critical dimension in the quenched models is shifted by two units upwards in comparison to their counterparts with white in-time noise. Possible scaling regimes associated with fixed points of the renormalization group equations are found and the critical exponents are derived to the leading order of the corresponding epsilon-expansions. Some exact values and relations for these exponents are obtained.