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The magneto-caloric effect (MCE), which is the refrigeration based on the variation of the magnetic entropy, is of great interest in both technological applications and fundamental research. The MCE is quantified by the magnetic Gruneisen parameter $Gamma_{textmd{mag}}$. We report on an analysis of $Gamma_{textmd{mag}}$ for the classical Brillouin-like paramagnet, for a modified Brillouin function taking into account a zero-field splitting originated from the spin-orbit (SO) interaction and for the one-dimensional Ising (1DI) model under longitudinal field. For both Brillouin-like model with SO interaction and the longitudinal 1DI model, for $ T rightarrow$ 0 and vanishing field a sign change of the MCE is observed, suggestive of a quantum phase transition. SO interaction leads to a narrowing of the critical fluctuations upon approaching the critical point. Our findings emphasize the relevance of $Gamma_{textmd{mag}}$ for exploring critical points. Also, we show that the Brillouin model with and without SO interaction can be recovered from the 1DI model in the regime of high-temperatures and vanishing coupling constant $J$.
At any quantum critical point (QCP) with a critical magnetic field $H_c$, the magnetic Gruneisen parameter $Gamma_{rm H}$, which equals the adiabatic magnetocaloric effect, is predicted to show characteristic signatures such as a divergence, sign cha
The Gruneisen ratio ($Gamma$), i.e.,the ratio of the linear thermal expansivity to the specific heat at constant pressure, quantifies the degree of anharmonicity of the potential governing the physical properties of a system. While $Gamma$ has been i
High-quality single crystals of CoTiO$_3$ are grown and used to elucidate in detail structural and magnetostructural effects by means of high-resolution capacitance dilatometry studies in fields up to 15 T which are complemented by specific heat and
We use the recently-proposed emph{compressible cell} Ising-like model [Phys. Rev. Lett. textbf{120}, 120603 (2018)] to estimate the ratio between thermal expansivity and specific heat (the Gruneisen parameter $Gamma$) in supercooled water. Near the c
A simple effective model of charge ordered and (or) magnetically ordered insulators is studied. The tight binding Hamiltonian analyzed consists of (i) the effective on-site interaction U, (ii) the intersite density-density interaction W and (iii) int