Effect of disorder on first-order phase transitions

Disorder is an inevitable part of any condensed matter system and therefore its study has always been of great importance. The effect of quenched randomness on a system that exhibits a continuous phase transition in the absence of any impurity has been studied in the past and the results are relatively well understood. However, the effect of quenched randomness on \emph{first-order} phase transitions is still not well understood. In this dissertation, we study the effect of quenched bond-randomness on the classical and quantum first-order phase transitions.In Chapter 2, we study the effect of the disordered three-color Ashkin-Teller model, whose pure version undergoes a first-order phase transition. We show that the rounding of the first-order transition of the pure model due to the impurities is manifested as a critical point. We conclusively rule out that the model belongs to the universality class of the two-dimensional Ising model. Furthermore, we find that the exponents $\beta$ and $\nu$ vary with disorder and the four-spin coupling strength.In Chapter 3, we extend our study of the disordered three-color Ashkin-Teller model. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to $128 \times 128$ spins, each of which is represented by three colors taking values $\pm 1$, we show that the rounding of the first-order phase transition is an emergent criticality.We find that the critical exponents, $\nu$ and $\beta$, change as the strength of disorder or the four-spin coupling varies, and we show that the correlation length critical exponent violates the lower bound $2/D \le \nu$, where $D$ is the dimension of the system.In Chapter 4, we study the \emph{quantum} three-color Ashkin--Teller model and show that the quantum critical point in $(1+1)$ dimension is an unusual one, with activated scaling at the critical point and Griffiths-McCoy phase away from it. We find that the behavior is similar to the transverse random field Ising model, even though the pure system has a first-order transition in this case