# Quantitative Assessment of the Toner and Tu Theory of Polar Flocks

## TL;DR

This paper quantitatively tests the Toner and Tu theory of polar flocks using large-scale simulations, confirming some predicted behaviors but also revealing significant discrepancies in scaling exponents and anisotropy at large scales.

## Contribution

It provides a detailed numerical assessment of the Toner and Tu theory, highlighting both its successes and limitations in describing active matter flocks.

## Key findings

- Confirmed the overall phenomenology and algebraic scaling predicted by Toner and Tu.
- Discovered significant differences in the estimated scaling exponents from the original conjecture.
- Identified a large crossover scale where flocks become weakly anisotropic.

## Abstract

We present a quantitative assessment of the Toner and Tu theory describing the universal scaling of fluctuations in polar phases of dry active matter. Using large scale simulations of the Vicsek model in two and three dimensions, we find the overall phenomenology and generic algebraic scaling predicted by Toner and Tu, but our data on density correlations reveal some qualitative discrepancies. The values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995. In particular, we identify a large crossover scale beyond which flocks are only weakly anisotropic. We discuss the meaning and consequences of these results.