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.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.

Jan 1, 20150 citations

Pseudo-critical phenomena in first-order phase transitions

博池田

Jan 1, 19800 citations

CRITICAL BEHAVIOR OF THE SEMI-INFINITE MIXED SPINS (7/2, 1/2) MODEL

Hasnae Saadi, El Mostafa Jalal, A. El Antari +3 more

By the use of the Migdal–Kadanoff renormalization group technique and the mean field approximation, we have explored the critical behavior of the semi-infinite mixed spin-7/2 and spin-1/2 Blume–Capel model. As a function of the computation ratios (bulk-surface) R and Y, different phase diagrams in the bulk and on the surface are classified and determined in the (surface anisotropy, temperature) plane. We have found four types of phase diagrams characterized by ordinary, extraordinary, surface, and special phase transitions. The derivative of the free energy and the behavior of the bulk and surface magnetizations are plotted at very low temperatures proving the existence of first-order transitions for both the surface and bulk. We have also presented the related fixed points and the critical exponents manifesting several classes of universality at the surface. Otherwise, a comparison was made between the two methods as well as with previous studies.By the use of the Migdal–Kadanoff renormalization group technique and the mean field approximation, we have explored the critical behavior of the semi-infinite mixed spin-7/2 and spin-1/2 Blume–Capel model. As a function of the computation ratios (bulk-surface) R and Y, different phase diagrams in the bulk and on the surface are classified and determined in the (surface anisotropy, temperature) plane. We have found four types of phase diagrams characterized by ordinary, extraordinary, surface, and special phase transitions. The derivative of the free energy and the behavior of the bulk and surface magnetizations are plotted at very low temperatures proving the existence of first-order transitions for both the surface and bulk. We have also presented the related fixed points and the critical exponents manifesting several classes of universality at the surface. Otherwise, a comparison was made between the two methods as well as with previous studies.

Surface Review and LettersJun 14, 20235 citations

Phase Transitions and Critical Phenomena

David A. Lavis, Roman Frigg

Fundamental theories of physicsJan 1, 202557 citations

The second order phase transitions and critical phenomena

WORLD SCIENTIFIC eBooksOct 3, 20182 citations

Dissipation-driven quantum phase transitions and symmetry breaking

Julia D. Hannukainen, Jonas Larson

By considering a solvable driven-dissipative quantum model, we demonstrate that continuous phase transitions in dissipative systems may occur without an accompanying symmetry breaking. As such, the underlying mechanism for this type of transition is qualitatively different from that of continuous equilibrium phase transitions. In our model, the transition is solely a result of the interplay between Hamiltonian and dissipative dynamics and manifests as a nonanalyticity in the steady state ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathrm{ss}}$ in the thermodynamic limit. Based on knowledge from critical classical models we suggest that this behavior derives from a rounding of a first-order phase transition into a continuous one due to large environment-induced fluctuations. Despite being conceptually different from the traditional continuous transitions, we show that expectations of local observables can still be characterized by a set of critical exponents.By considering a solvable driven-dissipative quantum model, we demonstrate that continuous phase transitions in dissipative systems may occur without an accompanying symmetry breaking. As such, the underlying mechanism for this type of transition is qualitatively different from that of continuous equilibrium phase transitions. In our model, the transition is solely a result of the interplay between Hamiltonian and dissipative dynamics and manifests as a nonanalyticity in the steady state ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathrm{ss}}$ in the thermodynamic limit. Based on knowledge from critical classical models we suggest that this behavior derives from a rounding of a first-order phase transition into a continuous one due to large environment-induced fluctuations. Despite being conceptually different from the traditional continuous transitions, we show that expectations of local observables can still be characterized by a set of critical exponents.

arXiv:1703.10238Physical Review AOct 15, 201881 citations

\\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.