# Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks

## TL;DR

This paper introduces a novel ferromagnetic model with a marginal potential to explain the coexistence of strong order and scale-free speed correlations in starling flocks, revealing a zero-temperature critical point.

## Contribution

The study proposes a new marginal ferromagnetic model that captures the anomalous correlations in bird flocks, highlighting a zero-temperature critical point not seen in standard models.

## Key findings

- Model reproduces scale-free speed correlations in flocks
- Zero-temperature critical point emerges in the model
- Divergent susceptibility and correlation length observed

## Abstract

We introduce a new ferromagnetic model capable of reproducing one of the most intriguing properties of collective behaviour in starling flocks, namely the fact that strong collective order of the system coexists with scale-free correlations of the modulus of the microscopic degrees of freedom, that is the birds' speeds. The key idea of the new theory is that the single-particle potential needed to bound the modulus of the microscopic degrees of freedom around a finite value, is marginal, that is has zero curvature. We study the model by using mean-field approximation and Monte Carlo simulations in three dimensions, complemented by finite-size scaling analysis. While at the standard critical temperature, $T_c$, the properties of the marginal model are exactly the same as a normal ferromagnet with continuous symmetry-breaking, our results show that a novel zero-temperature critical point emerges, so that in its deeply ordered phase the marginal model develops divergent susceptibility and correlation length of the modulus of the microscopic degrees of freedom, in complete analogy with experimental data on natural flocks of starlings.