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) ₂Cu 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 _{Γ E}, which quantifies the electrocaloric effect; and (iv) we identify the metallic/insulating coexistence region as an electronic Griffiths-like phase. Our findings suggest that _{Γ E} governs the dielectric response close to the critical point and that an electronic Griffiths-like phase emerges in the coexistence region.