We study the effects of uncorrelated quenched disorder to the phase diagram and continuous transitions of three-dimensional lattice Z_{2} gauge Higgs models. For this purpose, we consider two types of quenched disorder, associated with the sites and plaquettes of the cubic lattice. In both cases, for sufficiently weak disorder, the phase diagram remains similar to that of the pure system, showing two different phases (one of them being a topologically ordered phase), separated by two different continuous transition lines. However, the quenched disorder changes the universality classes of the critical behaviors along some of the transition lines. The random-plaquette disorder turns out to be relevant along the topological Z_{2} gauge transition line, so the critical behaviors belong to the different random-plaquette Z_{2} gauge (RPZ_{2}G) universality class with length-scale exponent ν=ν_{rp}≈0.82; on the other hand, it turns out to be irrelevant along the other Ising^{×} transition line (a variant of the Ising transitions with a gauge-dependent order parameter), leaving unchanged its asymptotic critical behaviors with ν=ν_{I}≈0.63. The random-site disorder leads to a substantially different scenario: it destabilizes the Ising^{×} critical behaviors of the pure model, changing them into those of the randomly dilute Ising^{×} (RDI^{×}) universality class with ν=ν_{RDI}≈0.68, while the critical behaviors along the other Z_{2} gauge topological transition line remains stable, with ν=ν_{I}≈0.63.
We study the effects of uncorrelated quenched disorder to the phase diagram and continuous transitions of three-dimensional lattice Z_{2} gauge Higgs models. For this purpose, we consider two types of quenched disorder, associated with the sites and plaquettes of the cubic lattice. In both cases, for sufficiently weak disorder, the phase diagram remains similar to that of the pure system, showing two different phases (one of them being a topologically ordered phase), separated by two different continuous transition lines. However, the quenched disorder changes the universality classes of the critical behaviors along some of the transition lines. The random-plaquette disorder turns out to be relevant along the topological Z_{2} gauge transition line, so the critical behaviors belong to the different random-plaquette Z_{2} gauge (RPZ_{2}G) universality class with length-scale exponent ν=ν_{rp}≈0.82; on the other hand, it turns out to be irrelevant along the other Ising^{×} transition line (a variant of the Ising transitions with a gauge-dependent order parameter), leaving unchanged its asymptotic critical behaviors with ν=ν_{I}≈0.63. The random-site disorder leads to a substantially different scenario: it destabilizes the Ising^{×} critical behaviors of the pure model, changing them into those of the randomly dilute Ising^{×} (RDI^{×}) universality class with ν=ν_{RDI}≈0.68, while the critical behaviors along the other Z_{2} gauge topological transition line remains stable, with ν=ν_{I}≈0.63.
We address issues related to the presence of defects at finite-temperature topological transitions, in particular when defects are modeled in terms of further variables associated with a quenched disorder, corresponding to the limit in which the defect dynamics is very slow. As a paradigmatic model, we consider the classical three-dimensional lattice Z_{2} gauge model in the presence of quenched uncorrelated disorder associated with the plaquettes of the lattice, whose topological transitions are characterized by the absence of a local order parameter. We study the critical behaviors in the presence of weak disorder. We show that they belong to a topological universality class that differs from those of known statistical models, and in particular different from that of the lattice Z_{2} gauge models without disorder, in agreement with the Harris criterium for the relevance of uncorrelated quenched disorder when the pure system undergoes a continuous transition with positive specific-heat critical exponent.
We study the phase diagram and critical behaviors of three-dimensional lattice Z2-gauge N-vector models, in which an N-component real field is minimally coupled with Z2-gauge link variables. These models are invariant under global O(N) and local Z2 transformations. They present three phases characterized by the spontaneous breaking of the global O(N) symmetry and by the different topological properties of the Z2-gauge correlations. We address the nature of the three transition lines separating the three phases. The theoretical predictions are supported by numerical finite-size scaling analyses of Monte Carlo data for the N=2 model. In this case, continuous transitions can be observed along both transition lines where the N-component spins order, in the regimes of small and large inverse gauge coupling K. Even though these continuous transitions belong to the same XY universality class, their critical modes turn out to be different. When the gauge variables are disordered (small K), the relevant order-parameter field is a gauge-invariant bilinear combination of the vector field. On the other hand, when the gauge variables are ordered (large K), the order-parameter field is the gauge-dependent N-vector field, whose critical behavior can only be probed by using a stochastic gauge fixing that reduces the gauge freedom.
We investigate the temperature-disorder (T-$\ensuremath{\sigma}$) phase diagram of a three-dimensional gauge glass model, which is a cubic-lattice nearest-neighbor XY model with quenched random phase shifts Axy at the bonds. We consider the uncorrelated phase-shift distribution $P({A}_{\mathit{xy}})~\mathrm{exp}[(\mathrm{cos}{A}_{\mathit{xy}})/\ensuremath{\sigma}]$, which has the pure XY model, and the uniform distribution of random phase shifts as extreme cases at $\ensuremath{\sigma}=0$ and $\ensuremath{\sigma}\ensuremath{\rightarrow}\ensuremath{\infty}$, respectively, and which gives rise to equal magnetic and overlap correlation functions when $T=\ensuremath{\sigma}$. Our study is mostly based on numerical Monte Carlo simulations. While the high-temperature phase is always paramagnetic, at low temperatures there is a ferromagnetic phase for weak disorder (small $\ensuremath{\sigma}$) and a glassy phase at large disorder (large $\ensuremath{\sigma}$). These three phases are separated by transition lines with different magnetic and glassy critical behaviors. The disorder induced by the random phase shifts turns out to be irrelevant at the paramagnetic-ferromagnetic transition line, where the critical behavior belongs to the 3D XY universality class of pure systems; disorder gives rise only to very slowly decaying scaling corrections. The glassy critical behavior along the paramagnetic-glassy transition line belongs to the gauge-glass universality class, with a quite large exponent $\ensuremath{\nu}=3.2(4)$. These transition lines meet at a multicritical point M, located at ${T}_{M}={\ensuremath{\sigma}}_{M}=0.7840(2)$. The low-temperature ferromagnetic and glassy phases are separated by a third transition line, from M down to the T=0 axis, which is slightly reentrant.
The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that the second-order transition emerging under bond randomness from the first-order regime of the pure model belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site and bond dilution). The second amounts to a strong violation of the universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.
The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-order regime of the pure model, belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site- and bond-dilution). The second, amounts to a strong violation of universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.
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 128times128 spins, each of which is represented by three colors taking values pm1, 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/Dlenu, 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.