Box scaling as a proxy of finite size correlations

MARTIN, DANIEL A.; RIBEIRO, TIAGO L.; CANNAS, SERGIO A.; GRIGERA, TOMAS S.; PLENZ, DIETMAR; CHIALVO, DANTE R.

Scientific Reports

Springer Nature

Año: 2021 vol. 11 p. 15937 - 15937

The scaling of correlations as a function of size provides important hints to understand criticalphenomena on a variety of systems. Its study in biological structures offers two challenges: usuallythey are not of infinite size, and, in the majority of cases, dimensions can not be varied at will.Here we discuss how finite-size scaling can be approximated in an experimental system of fixedand relatively small extent, by computing correlations inside of a reduced field of view of variouswidths (we will refer to this procedure as ?box-scaling?). A relation among the size of the field ofview, and measured correlation length, is derived at, and away from, the critical regime. Numericalsimulations of a neuronal network, as well as the ferromagnetic 2D Ising model, are used to verify suchapproximations. Numerical results support the validity of the heuristic approach, which should beuseful to characterize relevant aspects of critical phenomena in biological systems.