Griffiths-like phase close to the Mott transition

We explore the coexistence region in the vicinity of the Mott critical end point employing a compressible cell spin-$1/2$ Ising-like model. We analyze the case for the spin-liquid candidate $κ$-(BEDT-TTF)$2$Cu$2$(CN)$3$⁠, where close to the Mott critical end point metallic puddles coexist with an insulating ferroelectric phase. Our results are fourfold: (i) a universal divergent-like behavior of the Grüneisen parameter upon crossing the first-order transition line; (ii) based on scaling arguments, we show that within the coexistence region, for any system close to the critical point, the relaxation-time is entropy-dependent; (iii) we propose the electric Grüneisen parameter $ΓE$⁠, which quantifies the electrocaloric effect; and (iv) we identify the metallic/insulating coexistence region as an electronic Griffiths-like phase. Our findings suggest that $ΓE$ governs the dielectric response close to the critical point and that an electronic Griffiths-like phase emerges in the coexistence region.