# Temperature Dependence of Nonlinear Susceptibilities in an Infinite Range Interaction Model

## TL;DR

This paper models the magnetic properties of systems with many interacting spins, revealing how the number of spins affects susceptibility peaks, magnetization steps, and metamagnetic behavior, especially distinguishing between even and odd numbers of spins.

## Contribution

It introduces a model for analyzing nonlinear susceptibilities and metamagnetic properties in infinite-range interaction spin systems with arbitrary particle numbers.

## Key findings

- Susceptibilities show maxima at specific temperatures for even N.
- Odd N systems exhibit a free spin response dominating at low temperatures.
- Magnetization exhibits quantized steps depending on N and magnetic field.

## Abstract

We present a model to probe metamagnetic properties in systems with an arbitrary number of interacting spins. Thermodynamic properties such as the magnetization per particle $m(B,T,N)$, linear susceptibility $\chi_1(T)$, nonlinear susceptibilities $\chi_3(T)$ and $\chi_5(T)$, specific heat $C(B,T,N)$, and pressure $P(B,T,N)$ were calculated. The model produces a different magnetic response for $N$ particles when comparing to $N - 1$ particles for small $N \sim 1$. For an even number of particles, the susceptibilities show maxima in their temperature dependence. An odd number produces an additional free spin response that dominates at low temperatures. This free spin response for odd $N$ also produces a step in the magnetization per particle at $B = 0$. The magnetization shows $N/2$ steps at $\gamma B_c/J = n$ with integer $n$ for even $N$ and $(N-1)/2$ additional steps at half-integer $n$ starting at 3/2 for odd $N$. Small clusters respond with metamagnetism in an otherwise isotropic spin space, while the large clusters show no metamagnetism.