arXiv subjects

F. Igloi

Publications and source records attributed to F. Igloi.

At least 19 recordsLinked to original sources

arXiv2010

Interface mapping in two-dimensional random lattice models

We consider two disordered lattice models on the square lattice: on the medial lattice the random field Ising model at T=0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface properties of the two models are known to be related by a mapping which is valid in the continuum approximation. Here we consider finite random samples with the same form of disorder for both models and calculate the respective equilibrium states exactly by combinatorial optimization algorithms. We study the evolution of the interfaces with the strength of disorder and analyse and compare the interfaces of the two models in finite lattices.

cond-mat.stat-mech↗

arXiv2009

Nonequilibrium dynamics of fully frustrated Ising models at T=0

We consider two fully frustrated Ising models: the antiferromagnetic triangular model in a field of strength, $h=H T k_B$, as well as the Villain model on the square lattice. After a quench from a disordered initial state to T=0 we study the nonequilibrium dynamics of both models by Monte Carlo simulations. In a finite system of linear size, $L$, we define and measure sample dependent "first passage time", $t_r$, which is the number of Monte Carlo steps until the energy is relaxed to the ground-state value. The distribution of $t_r$, in particular its mean value, $< t_r(L) >$, is shown to obey the scaling relation, $< t_r(L) > \sim L^2 \ln(L/L_0)$, for both models. Scaling of the autocorrelation function of the antiferromagnetic triangular model is shown to involve logarithmic corrections, both at H=0 and at the field-induced Kosterlitz-Thouless transition, however the autocorrelation exponent is found to be $H$ dependent.

cond-mat.stat-mech↗

arXiv2008

Entanglement in spin chains with gradients

We study solvable spin chains where either fields or couplings vary linearly in space and create a sandwich-like structure of the ground state. We find that the entanglement entropy between two halves of a chain varies logarithmically with the interface width. After quenching to a homogeneous critical system, the entropy grows logarithmically in time in the XX model, but quadratically in the transverse Ising chain. We explain this behaviour and indicate generalizations to other power laws.

cond-mat.stat-mech↗

arXiv2008

Aperiodic Ising model on the Bethe lattice: Exact results

We consider the Ising model on the Bethe lattice with aperiodic modulation of the couplings, which has been studied numerically in Phys. Rev. E 77, 041113 (2008). Here we present a relevance-irrelevance criterion and solve the critical behavior exactly for marginal aperiodic sequences. We present analytical formulae for the continuously varying critical exponents and discuss a relationship with the (surface) critical behavior of the aperiodic quantum Ising chain.

cond-mat.stat-mech↗

arXiv2008

Density of critical clusters in strips of strongly disordered systems

We consider two models with disorder dominated critical points and study the distribution of clusters which are confined in strips and touch one or both boundaries. For the classical random bond Potts model in the large-q limit we study optimal Fortuin-Kasteleyn clusters by combinatorial optimization algorithm. For the random transverse-field Ising chain clusters are defined and calculated through the strong disorder renormalization group method. The numerically calculated density profiles close to the boundaries are shown to follow scaling predictions. For the random bond Potts model we have obtained accurate numerical estimates for the critical exponents and demonstrated that the density profiles are well described by conformal formulae.

cond-mat.stat-mech↗

arXiv2007

Entanglement entropy of aperiodic quantum spin chains

We study the entanglement entropy of blocks of contiguous spins in non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg, XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and relevant aperiodic modulations, the entanglement entropy is found to be a logarithmic function of the block size with log-periodic oscillations. The effective central charge, c_eff, defined through the constant in front of the logarithm may depend on the ratio of couplings and can even exceed the corresponding value in the homogeneous system. In the strong modulation limit, the ground state is constructed by a renormalization group method and the limiting value of c_eff is exactly calculated. Keeping the ratio of the block size and the system size constant, the entanglement entropy exhibits a scaling property, however, the corresponding scaling function may be nonanalytic.

cond-mat.stat-mech↗

arXiv2006

Critical behavior at the interface between two systems belonging to different universality classes

We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We solve this problem analytically in the frame of mean-field theory, which is then generalized using phenomenological scaling considerations. A large variety of interface critical behavior is obtained which is checked numerically on the example of two-dimensional q-state Potts models with q=2 to 4. Weak interface couplings are generally irrelevant, resulting in the same critical behavior at the interface as for a free surface. With strong interface couplings, the interface remains ordered at the bulk transition temperature. More interesting is the intermediate situation, the special interface transition, when the critical behavior at the interface involves new critical exponents, which however can be expressed in terms of the bulk and surface exponents of the two subsystems. We discuss also the smooth or discontinuous nature of the order parameter profile.

cond-mat.stat-mech↗

arXiv2005

Two-dimensional Ising model with self-dual biaxially correlated disorder

We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder represents a relevant perturbation according to the extended Harris criterion. Critical properties of the system are studied by large scale Monte Carlo simulations. The correlation length critical exponent, ν=2.005(5), corresponds to that expected in a system with isotropic correlated long-range disorder, whereas the scaling dimension of the magnetization density, x_m=0.1294(7), is somewhat larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined numerically.

cond-mat.stat-mech↗

arXiv2005

Partially asymmetric exclusion models with quenched disorder

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated distance traveled by the particles, x, scales with the time, t, as x ~ t^{1/z}, with a dynamical exponent z > 0. Using extreme value statistics and an asymptotically exact strong disorder renormalization group method we analytically calculate, z_{pt}, for particlewise (pt) disorder, which is argued to be related to the dynamical exponent for sitewise (st) disorder as z_{st}=z_{pt}/2. In the symmetric situation with zero mean drift the particle diffusion is ultra-slow, logarithmic in time.

cond-mat.dis-nn↗

arXiv2004

Logarithmic corrections in the two-dimensional Ising model in a random surface field

In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The calculated effective (temperature or size dependent) critical exponents fit with the field-theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system's critical behaviour.

cond-mat.stat-mech↗

arXiv2002

Phase transition in the 2d random Potts model in the large-q limit

Phase transition in the two-dimensional $q$-state Potts model with random ferromagnetic couplings in the large-q limit is conjectured to be described by the isotropic version of the infinite randomness fixed point of the random transverse-field Ising spin chain. This is supported by extensive numerical studies with a combinatorial optimization algorithm giving estimates for the critical exponents in accordance with the conjectured values: $β=(3-\sqrt{5})/4$, $β_s=1/2$ and $ν=1$. The specific heat has a logarithmic singularity, but at the transition point there are very strong sample-to-sample fluctuations. Discretized randomness results in discontinuities in the internal energy.

cond-mat.stat-mech↗

arXiv2002

Surface-induced disorder and aperiodic perturbations at first-order transitions

In systems displaying a bulk first-order transition the order parameter may vanish continuously at a free surface, a phenomenon which is called surface-induced disorder. In the presence of surface-induced disorder the correlation lengths, parallel and perpendicular to the surface, diverge at the bulk transition point. In this way the surface induces an anisotropic power-law singular behavior for some bulk quantities. For example in a finite system of transverse linear size L, the response functions diverge as L^{(d-1)z+1}, where d is the dimension of the system and z is the anisotropy exponent. We present a general scaling picture for this anisotropic discontinuity fixed point. Our phenomenological results are confronted with analytical and numerical calculations on the 2D q-state Potts model in the large-q limit. The scaling results are demonstrated to apply also for the same model with a layered, Fibonacci-type modulation of the couplings for which the anisotropy exponent is a continuous function of the strength of the quasiperiodic perturbation.

cond-mat.stat-mech↗

arXiv2002

Optimal Cooperation and Submodularity for Computing Potts' Partition Functions with a Large Number of State

The partition function of the q-state Potts model with random ferromagnetic couplings in the large-q limit is generally dominated by the contribution of a single diagram of the high temperature expansion. Computing this dominant diagram amounts to minimizing a particular submodular function. We provide a combinatorial optimization algorithm, the optimal cooperation algorithm, which works in polynomial time for any lattice. Practical implementation and the speed of the method is also discussed.

cond-mat.stat-mech↗

arXiv2001

Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model

We consider m two-dimensional semi-infinite planes of Ising spins joined together through surface spins and study the critical behaviour near to the junction. The m=0 limit of the model - according to the replica trick - corresponds to the semi-infinite Ising model in the presence of a random surface field (RSFI). Using conformal mapping, second-order perturbation expansion around the weakly- and strongly-coupled planes limits and differential renormalization group, we show that the surface critical behaviour of the RSFI model is described by Ising critical exponents with logarithmic corrections to scaling, while at multiple junctions (m>2) the transition is first order. There is a spontaneous junction magnetization at the bulk critical point.

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arXiv2000

Conformal Profiles in the Hilhorst--van Leeuwen Model

We study the critical energy and magnetization profiles for the Ising quantum chain with a marginal extended surface perturbation of the form A/y, y being the distance from the surface (Hilhorst-van Leeuwen model). For weak local couplings, A A_c, there is surface order at the bulk critical point. If conformal invariance is assumed to hold with such marginal perturbations, it predicts conformal profiles with the same scaling form as for the unperturbed quantum chain, with marginal surface exponents replacing the unperturbed ones. The results of direct analytical and numerical calculations of the profiles confirm the validity of the conformal expressions in the regimes of second- and first-order surface transitions.

cond-mat.stat-mech↗

arXiv2000

Long range correlations in the non-equilibrium quantum relaxation of a spin chain

We consider the non-stationary quantum relaxation of the Ising spin chain in a transverse field of strength h. Starting from a homogeneously magnetized initial state the system approaches a stationary state by a process possessing quasi long range correlations in time and space, independent of the value of $h$. In particular the system exhibits aging (or lack of time translational invariance on intermediate time scales) although no indications of coarsening are present.

cond-mat.stat-mech↗

arXiv1999

Numerical renormalization group study of random transverse Ising models in one and two space dimensions

The quantum critical behavior and the Griffiths-McCoy singularities of random quantum Ising ferromagnets are studied by applying a numerical implementation of the Ma-Dasgupta-Hu renormalization group scheme. We check the procedure for the analytically tractable one-dimensional case and apply our code to the quasi-one-dimensional double chain. For the latter we obtain identical critical exponents as for the simple chain implying the same universality class. Then we apply the method to the two-dimensional case for which we get estimates for the exponents that are compatible with a recent study in the same spirit.

cond-mat.dis-nn↗

arXiv1999

Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions

We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confronted with numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L<=512) are found to follow conformal predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution show multi-scaling character. In the Griffiths phase, which is an extended part of the off-critical region average autocorrelations have a power-law form with a non-universal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.

cond-mat.dis-nn↗