arXiv subjects

Nikolaos G. Fytas

Publications and source records attributed to Nikolaos G. Fytas.

At least 19 recordsLinked to original sources

arXiv2026

Crossover and universality breaking in the dilute Baxter-Wu model

The critical behavior of the Baxter-Wu model belongs to the universality class of the four-state Potts model. While the introduction of annealed vacancies does not alter the criticality of the four-state Potts model, the dilute Baxter-Wu model has remained the subject of several competing scenarios. Here we investigate the phase diagram of the spin-$1$ Baxter-Wu model in the presence of a crystal field using transfer-matrix calculations and large-scale Monte Carlo simulations. Our results reveal a systematic evolution of the effective critical behavior with increasing crystal field, accompanied by increasingly strong finite-size corrections near the crossover to the first-order regime. Along the line of continuous transitions, the central charge remains close to $c=1$, while the scaling dimensions systematically deviate from the spin-$1/2$ limit as the crystal field increases, consistent with either continuously varying effective critical exponents or a slow crossover between competing critical behaviors. The first-order regime is independently characterized through multicanonical simulations, which confirm the expected finite-size scaling and interfacial behavior. Taken together, our results provide a unified picture of the dilute spin-$1$ Baxter-Wu model, substantially narrowing the range of possible scenarios for the crossover between continuous and first-order phase transitions.

cond-mat.stat-mech↗

arXiv2026

Cluster Dynamics Stay Fast-Until Tricriticality

Cluster Monte Carlo algorithms are widely regarded as the most effective route to overcoming critical slowing down in lattice spin systems. Whether this acceleration persists in the presence of vacancies and multicritical fluctuations, however, remains unresolved. We address this question through a systematic dynamic-scaling study of hybrid cluster-local update schemes in the two-dimensional Blume-Capel model, which exhibits a line of continuous Ising-like transitions terminating at a tricritical point. Along the entire critical line, hybrid dynamics retain the near-optimal efficiency of pure cluster updates despite the presence of annealed vacancies. Strikingly, this acceleration collapses precisely at tricriticality, where the dynamic critical exponent reverts to the local-update value. We trace this breakdown to the correlated percolation of vacancies, whose emergent system-spanning geometry obstructs nonlocal relaxation in the spin sector. Our results identify a fundamental geometric limitation of cluster acceleration at tricriticality and establish vacancy percolation as the mechanism controlling dynamic universality in hybrid Monte Carlo dynamics.

cond-mat.stat-mech↗

arXiv2026

Competing ferromagnetic and antiferromagnetic phases on the frustrated Ising honeycomb lattice

We investigate the frustrated $J_1$-$J_2$-$J_3$ Ising model on the honeycomb lattice, featuring first- and second-neighbor ferromagnetic couplings ($J_1>0$ and $J_2>0$) and third-neighbor antiferromagnetic interactions ($J_3<0$). Using the cluster mean-field method, we analyze the phase transitions in the regime $1/2 < J_2/J_1 \le 1$, where ferromagnetic and antiferromagnetic phases compete. Our results reveal that near the strongly frustrated limit $J_3/J_1 = -1$, the system exhibits order-by-disorder state selection, tricritical and bicritical behavior, critical endpoints, and two successive phase transitions. The ferromagnetic-paramagnetic transition remains second order across the entire interaction range, whereas the antiferromagnetic-paramagnetic boundary shows a richer behavior, including both first- and second-order transitions as well as tricriticality. Increasing the second-neighbor coupling $J_2/J_1$ narrows the range of $J_3/J_1$ where first-order antiferromagnetic-paramagnetic transitions occur; beyond a certain threshold, only second-order order-disorder transitions persist. Consequently, the tricritical point shifts toward $J_3/J_1 \approx -1$ as $J_2/J_1$ increases, culminating in a bicritical point where the antiferromagnetic, ferromagnetic, and paramagnetic phases meet.

cond-mat.stat-mech↗

arXiv2026

Cluster percolation and dynamical scaling in the Baxter--Wu model

We investigate the percolation behavior of Fortuin-Kasteleyn--type clusters in the spin-$1/2$ Baxter--Wu model with three-spin interactions on a triangular lattice. The considered clusters are constructed by randomly freezing one of the three sublattices, resulting in effective pairwise interactions among the remaining spins. Using Monte Carlo simulations combined with a finite-size scaling analysis, we determine the percolation temperature of these stochastic clusters and show that it coincides with the exact thermal critical point of the model. The critical exponents derived from cluster observables are consistent with those of the underlying thermal phase transition. Finally, we analyze the dynamical scaling of the multi-cluster and single-cluster algorithms resulting from the cluster construction, highlighting their efficiency and scaling behavior with system size.

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arXiv2025

Transfer-matrix approach to the Blume-Capel model on the triangular lattice

We investigate the spin-$1$ Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact spectra for strip widths up to $L = 19$, we accurately locate the tricritical point improving upon recent Monte Carlo estimates. In the first-order regime, we observe exponential scaling of the spectral gap, reflecting the linear growth of interfacial tension as the temperature decreases below the tricritical point. Finally, we validate our tricritical point estimate through precise agreement with conformal field theory predictions for the tricritical Ising universality class. Our results underscore the continued utility of the transfer-matrix approach for studying phase transitions in complex lattice models.

cond-mat.stat-mech↗

arXiv2025

Universal exotic dynamics in critical mesoscopic systems: Simulating the square root of Avogadro's number of spins

We explicitly demonstrate the universality of critical dynamics through unprecedented large-scale GPU-based simulations of two out-of-equilibrium processes, comparing the behavior of spin-$1/2$ Ising and spin-$1$ Blume-Capel models on a square lattice. In the first protocol, a completely disordered system is instantaneously brought into contact with a thermal bath at the critical temperature, allowing it to evolve until the coherence length exceeds $10^{3}$ lattice spacings. Finite-size effects are negligible due to the mesoscopic scale of the lattice sizes studied, with linear dimensions up to $L=2^{22}$ and $2^{19}$ for the Ising and Blume-Capel models, respectively. Our numerical data, and the subsequent analysis, demonstrate a strong dynamic universality between the two models and provide the most precise estimate to date of the dynamic critical exponent for this universality class, $z = 2.1676(1)$. In the second protocol, we corroborate the role of the universal ratio of dynamic and static length scales in achieving an exponential acceleration in the approach to equilibrium just \emph{above} the critical temperature, through a time-dependent variation of the thermal bath temperature. The results presented in this work leverage our CUDA-based numerical code, breaking the world record for the simulation speed of the Ising model.

cond-mat.stat-mech↗

arXiv2025

Massive-Scale Simulations of 2D Ising and Blume-Capel Models on Rack-Scale Multi-GPU Systems

We present high-performance implementations of the two-dimensional Ising and Blume-Capel models for large-scale, multi-GPU simulations. Our approach takes full advantage of the NVIDIA GB200 NVL72 system, which features up to $72$ GPUs interconnected via high-bandwidth NVLink, enabling direct GPU-to-GPU memory access across multiple nodes. By utilizing Fabric Memory and an optimized Monte Carlo kernel for the Ising model, our implementation supports simulations of systems with linear sizes up to $L=2^{23}$, corresponding to approximately $70$ trillion spins. This allows for a peak processing rate of nearly $1.15 \times 10^5$ lattice updates per nanosecond-setting a new performance benchmark for Ising model simulations. Additionally, we introduce a custom protocol for computing correlation functions, which strikes an optimal balance between computational efficiency and statistical accuracy. This protocol enables large-scale simulations without incurring prohibitive runtime costs. Benchmark results show near-perfect strong and weak scaling up to $64$ GPUs, demonstrating the effectiveness of our approach for large-scale statistical physics simulations.

physics.comp-ph↗

arXiv2025

Tricriticality and finite-size scaling in the triangular Blume-Capel ferromagnet

We report on numerical simulations of the two-dimensional spin-$1$ Blume-Capel ferromagnet embedded in a triangular lattice. Utilizing a range of Monte Carlo and finite-size scaling techniques, we explore several critical aspects along the crystal field--temperature ($Δ, T$) transition line. Wang-Landau simulations measuring the joint density of states in combination with the method of field mixing allow us to probe the phase coexistence curve in high resolution, determining the tricritical point $(Δ_{\rm t}, T_{\rm t})$ with improved accuracy and verifying the tricritical exponents. Extensive multicanonical simulations identifying transition points across the phase diagram characterize the Ising universality class for $Δ< Δ_{\rm t}$ with precise determination of thermal and magnetic critical exponents expected in the second-order regime. On the other hand, for $Δ> Δ_{\rm t}$, a finite-size scaling analysis is dedicated to revealing the first-order signature in the surface tension that linearly increases upon lowering the temperature deeper into the first-order transition regime. Finally, a comprehensive picture of the phase diagram for the model is presented, collecting transition points obtained from the combined numerical approach in this study and previous estimates in the literature.

cond-mat.stat-mech↗

arXiv2024

Monte Carlo study of the two-dimensional kinetic Ising model under a nonantisymmetric magnetic field

We present a comprehensive numerical study of dynamic phase transitions in the two-dimensional kinetic Ising model under a non-antisymmetric time-dependent magnetic field including a sinusoidal term and a second harmonic component. We demonstrate that the expected antisymmetric property and the scaling behavior of the order parameter are maintained using the recently proposed generalized conjugate field approach. Via a detailed finite-size scaling analysis we compute, for zero-bias field, the set of critical exponents suggesting that the Ising universality class is conserved, even in the absence of half-wave antisymmetry in the time-dependent magnetic field. Our results verify up-to-date experimental observations and provide a deeper understanding of non-equilibrium phase transitions, establishing a broader framework for exploring symmetry-breaking phenomena in driven magnetic systems.

cond-mat.stat-mech↗

arXiv2024

Critical and tricritical behavior of the $d=3$ Blume-Capel model: Results from small-scale Monte Carlo simulations

We investigate the location of the critical and tricritical points of the three-dimensional Blume-Capel model by analyzing the behavior of the first Lee-Yang zero, the density of partition function zeros, and higher-order cumulants of the magnetization. Our analysis is conducted through Monte Carlo simulations, intentionally using only small system sizes. We demonstrate that this approach yields excellent results for studying the critical behavior of the model. Our findings indicate that at the tricritical point, where logarithmic corrections are anticipated, the numerical results align closely with the theoretical exponents describing these corrections. These expected values are then employed to accurately determine the coordinates of the tricritical point. At the model's critical point, the corrections correspond to those of the three-dimensional Ising model criticality, which we also use to precisely ascertain the critical temperature at zero crystal field. Additionally, we utilize more traditional thermodynamic quantities to validate the self-consistency of our analysis.

cond-mat.stat-mech↗

arXiv2024

Dynamical critical behavior of the two-dimensional three-state Potts model

We investigate the dynamical critical behavior of the two-dimensional three-state Potts model with single spin-flip dynamics in equilibrium. We focus on the mean-squared deviation of the magnetization $M$ (MSD$_{M}$) as a function of time, as well as on the autocorrelation function of $M$. Our simulations reveal the existence of two crossover behaviors at times $τ_1 \sim L^{z_1}$ and $τ_2 \sim L^{z_2}$, separating three dynamical regimes. MSD$_{M}$ appears to shift from ordinary diffusion in the first regime, to anomalous diffusion in the second, and finally to be constant in the third regime. The magnetization autocorrelation function on the other hand is found to fluctuate between exponential decay, stretched-exponential decay, and then again exponential decay along these three regimes. This behavior is in agreement with the one reported recently for the two-dimensional Ising ferromagnet [Phys. Rev. E {\bf 108}, 034118 (2023)], indicating that the existence of two dynamic critical exponents is not a peculiarity of the Ising model itself. A comparison of both MSD$_{M}$ and the magnetization's autocorrelation function suggests that within our numerical accuracy the exponents $z_1$ and $z_2$ are shared between the Ising and three-state Potts models at least for the particular case of single spin-flip dynamics studied here, even though their equilibrium universality classes are clearly distinct. Continuity of MSD$_{M}$ requires that $α(z_2 - z_1) = γ/ν- z_1$, in which $α$ is the anomalous exponent in the intermediate regime. Since the ratio $γ/ν$ is not shared between the two models, it follows that $α$ is not shared either, an aspect well verified in our simulations. Finally, we also discuss the relevance of our main findings using another useful observable, namely the line magnetization $M_{l}$.

cond-mat.stat-mech↗

arXiv2024

Thermodynamic properties of disordered quantum spin ladders

In this paper, we study the thermodynamic properties of spin-$1/2$ antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths $r$, from the clean ($r=0$) case up to the diluted ($r \rightarrow 1$) limit, and for selected choices of number of legs $L_y$ per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in $r$, as well as a variable dependence of the spin gap in the amount of disorder upon increasing $L_y$.

cond-mat.stat-mech↗

arXiv2024

Geometric clusters in the overlap of the Ising model

We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two distinct types of clusters in the overlap, which we dub soft- and hard-constraint clusters, and which are subsets of the regions of constant spin overlap. By means of Monte Carlo simulations and a finite-size scaling analysis we estimate the transition temperature as well as the set of critical exponents characterizing the percolation transitions undergone by these two cluster types. The results suggest that both soft- and hard-constraint clusters percolate at the critical temperature of the Ising model and their critical behavior is governed by the correlation-length exponent $ν= 1$ found by Onsager. At the same time, they exhibit non-standard and distinct sets of exponents for the average cluster size and percolation strength.

cond-mat.stat-mech↗

arXiv2023

Finite-size scaling of the random-field Ising model above the upper critical dimension

Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In the present manuscript we address this problem in the even more complicated case of disordered systems. In particular, we investigate the scaling behavior of the random-field Ising model at dimension $D = 7$, i.e., above its upper critical dimension $D_{\rm u} = 6$, by employing extensive ground-state numerical simulations. Our results confirm the hypothesis that at dimensions $D > D_{\rm u}$, linear length scale $L$ should be replaced in finite-size scaling expressions by the effective scale $L_{\rm eff} = L^{D / D_{\rm u}}$. Via a fitted version of the quotients method that takes this modification, but also subleading scaling corrections into account, we compute the critical point of the transition for Gaussian random fields and provide estimates for the full set of critical exponents. Thus, our analysis indicates that this modified version of finite-size scaling is successful also in the context of the random-field problem.

cond-mat.stat-mech↗

arXiv2023

Critical dynamical behavior of the Ising model

We investigate the dynamical critical behavior of the two- and three-dimensional Ising model with Glauber dynamics in equilibrium. In contrast to the usual standing, we focus on the mean-squared deviation of the magnetization $M$, MSD$_M$, as a function of time, as well as on the autocorrelation function of $M$. These two functions are distinct but closely related. We find that MSD$_M$ features a first crossover at time $τ_1 \sim L^{z_{1}}$, from ordinary diffusion with MSD$_M$ $\sim t$, to anomalous diffusion with MSD$_M$ $\sim t^α$. Purely on numerical grounds, we obtain the values $z_1=0.45(5)$ and $α=0.752(5)$ for the two-dimensional Ising ferromagnet. Related to this, the magnetization autocorrelation function crosses over from an exponential decay to a stretched-exponential decay. At later times, we find a second crossover at time $τ_2 \sim L^{z_{2}}$. Here, MSD$_M$ saturates to its late-time value $\sim L^{2+γ/ν}$, while the autocorrelation function crosses over from stretched-exponential decay to simple exponential one. We also confirm numerically the value $z_{2}=2.1665(12)$, earlier reported as the single dynamic exponent. Continuity of MSD$_M$ requires that $α(z_{2}-z_{1})=γ/ν-z_1$. We speculate that $z_{1} = 1/2$ and $α= 3/4$, values that indeed lead to the expected $z_{2} = 13/6$ result. A complementary analysis for the three-dimensional Ising model provides the estimates $z_{1} = 1.35(2)$, $α=0.90(2)$, and $z_{2} = 2.032(3)$. While $z_{2}$ has attracted significant attention in the literature, we argue that for all practical purposes $z_{1}$ is more important, as it determines the number of statistically independent measurements during a long simulation.

cond-mat.stat-mech↗

arXiv2023

Disorder effects on the metastability of classical Heisenberg ferromagnets

In the present work, we investigate the effects of disorder on the reversal time ($τ$) of classical anisotropic Heisenberg ferromagnets in three dimensions by means of Monte Carlo simulations. Starting from the pure system, our analysis suggests that $τ$ increases with increasing anisotropy strength. On the other hand, for the case of randomly distributed anisotropy, generated from various statistical distributions, a set of results is obtained: (i) For both bimodal and uniform distributions the variation of $τ$ with the strength of anisotropy strongly depends on temperature. (ii) At lower temperatures, the decrement in $τ$ with increasing width of the distribution is more prominent. (iii) For the case of normally distributed anisotropy, the variation of $τ$ with the width of the distribution is non-monotonic, featuring a minimum value that decays exponentially with the temperature. Finally, we elaborate on the joint effect of longitudinal ($h_z$) and transverse ($h_x$) fields on $τ$, which appear to obey a scaling behavior of the form $τh_z^{n} \sim f(h_x)$.

cond-mat.stat-mech↗

arXiv2022

Transient behavior of damage spreading in the two-dimensional Blume-Capel ferromagnet

We study the transient behavior of damage propagation in the two-dimensional spin-$1$ Blume-Capel model using Monte Carlo simulations with Metropolis dynamics. We find that, for a particular region in the second-order transition regime of the crystal field--temperature phase diagram of the model, the average Hamming distance decreases exponentially with time in the weakly damaged system. Additionally, its rate of decay appears to depend linearly on a number of Hamiltonian parameters, namely the crystal field, temperature, applied magnetic field, but also on the amount of damage. Finally, a comparative study using Metropolis and Glauber dynamics indicates a slower decay rate of the average Hamming distance for the Glauber protocol.

cond-mat.stat-mech↗

arXiv2022

Universality in the two-dimensional dilute Baxter-Wu model

We study the question of universality in the two-dimensional spin-$1$ Baxter-Wu model in the presence of a crystal field $Δ$. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of $Δ$ and a parallelized variant of the multicanonical approach performed at constant temperature $T$. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the $(Δ, T)$ phase diagram indicates that the transition belongs to the universality class of the $4$-state Potts model. Previous controversies with respect to the nature of the transition are discussed and possibly attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model.

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