Absence of temperature-driven first-order phase transitions in systems with random bonds (invited)

Temperature‐driven first‐order phase transitions that involve symmetry breaking are converted to second order by the introduction of infinitesimal quenched bond randomness in spatial dimensions d≤2 or d≤4, respectively, for systems of n=1 or n≥ (R18)2 component microscopic degrees of freedom. Even strongly first‐order transitions undergo this conversion to second order! Above these dimensions, this phenomenon still occurs, but requires a threshold amount of bond randomness. For example, under bond randomness, the phase transitions of q‐state Potts models are second order for all q in d≤2. If no symmetry breaking is involved, temperature‐driven first‐order phase transitions are eliminated under the above conditions. Another consequence is that bond randomness drastically alters multicritical phase diagrams. Tricritical points and critical endpoints are entirely eliminated (d≤2) or depressed in temperature (d≳2). Similarly, bicritical phase diagrams are converted (d≤2) to reentrant‐disorder‐line or decouple...