Dynamic specific heat of frustrated Ising spin rings

Abstract

The dynamic specific heat C($\omega )$ is calculated exactly for rings of six coupled Ising spins within Glauber dynamics. We used the response of the internal energy to small temperature oscillations to find C($\omega )$. The spin glass (SG) and disordered ferromagnetic (DFM) rings showed here have four energy minima and thus four diverging relaxation times in the time evolution of magnetization and three such times in the evolution of energy. The properties of the real and imaginary parts of dynamic specific heat are investigated for different temperatures and frequencies. The dynamic susceptibility is affected by the longest relaxing mode while the dynamic specific heat is not. Our results confirm that C($\omega )$ is sensitive only to rapidly relaxing processes for ferromagnetic~(FM) and anti-ferromagnetic (AFM) cases.