arXiv subjects

Víctor Martín-Mayor

Publications and source records attributed to Víctor Martín-Mayor.

11 recordsLinked to original sources

arXiv2026

Low energy excitations in a long prism geometry: testing the lower critical dimension of the Ising spin glass

We propose a general method for studying systems that display low-energy excitations in their low-temperature phase. We argue that in a rectangular right-prism geometry (the 3-dimensional generalization of a strip), with one longitudinal size much larger than the transverse size, correlations decay exponentially (at all temperatures) along the longitudinal direction. Still, the scaling of the correlation length with the transverse size carries crucial information from which the lower critical dimension can be inferred. The method is applied in the particularly demanding context of Ising spin glasses at zero magnetic field. The lower critical dimension and the multifractal spectrum for the correlation functions are computed from large-scale numerical simulations. Several technical novelties (such as the unexpectedly crucial performance of Houdayer's cluster method or the convenience of using open---rather than periodic---boundary conditions) allow us to study three-dimensional prisms with transverse dimensions up to $L=24$ and effectively infinite longitudinal dimensions, down to low temperatures. The value that we find for the exponent controlling the behavior of the correlation length agrees with predictions from the Replica Symmetry Breaking (RSB) theory. We argue that our novel setting holds promise in clarifying which of the two competing theories, RSB or the Droplet Model, more accurately describes three-dimensional spin glasses.

cond-mat.dis-nn↗

arXiv2026

Cluster moves with an entropic reservoir accelerate low-temperature simulations of three-dimensional spin glasses

We present an algorithm for the simulation of three-dimensional spin glasses deep in the low-temperature phase: Parallel Tempering enhanced with Houdayer moves and with an entropic reservoir (PTHR). Although differences with the standard Houdayer algorithm are small, PTHR allows us to equilibrate a large number of samples of $L=16$ lattices with Gaussian couplings for temperatures $T\geq 0.2$. We show that the computational complexity displays better size scaling than standard Parallel Tempering. For finite sizes, our method outperforms other cluster algorithms by a speedup factor of around 64. In close analogy with standard Parallel Tempering, PTHR's computational complexity strongly relates to temperature chaos.

cond-mat.dis-nn↗

arXiv2026

On the true low-energy excitations of the three-dimensional spin glass

We study the low-energy excitations of the three dimensional spin glass through a large-scale Monte Carlo simulation on lattices up to $L=18$. We find smooth extrapolations down to zero temperature, which, in the case of the energy and of the link overlap, can be directly -- and favourably -- compared with previous investigations featuring ground states (i.e., at zero temperature). The best fit for the fractal dimension of the excitations is provided by Replica-Symmetry Breaking theory, but we also consider the alternative TNT description. The $P(q)$ is found to verify the Parisi-Toulouse temperature scaling. Our data provides a spectacular confirmation of the overlap-equivalence hypothesis.

cond-mat.dis-nn↗

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

Unraveling anomalous relaxation effects in the thermodynamic limit

We address two central open problems in the theory of anomalous Mpemba-like relaxations: their extension beyond one spatial dimension and their consistent formulation in the thermodynamic limit. Our framework is the antiferromagnetic Ising model on a square lattice under an externally applied magnetic field, which enables us to work in the presence of a phase transition. The rich phase diagram contains two control parameters: temperature and magnetic field. We demonstrate that the standard assumption of relaxation dominated by a single leading exponential is inconsistent for intensive observables exhibiting standard fluctuations. Instead, as the system size increases, a continuous spectrum of time scales emerges. Nevertheless, we make the ansatz that, in the vicinity of the phase transition, the spectral projector onto the slowest time scales can be effectively characterized in terms of an equilibrium thermodynamic quantity: the susceptibility associated with the order parameter of the metastable phase. Combined with the richness of the phase diagram, this ansatz yields qualitative and semi-quantitative predictions for optimal protocols leading to a variety of anomalous relaxation phenomena involving simultaneous variations of temperature and magnetic field. These include direct and inverse Mpemba effects, cooling-heating asymmetries, and faster heating induced by precooling. Careful Monte Carlo simulations validate our theoretical predictions. Furthermore, minimal post-optimization suffices to convert our analytically guided protocols into fully optimal ones that display anomalous relaxations in their most pronounced form.

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↗

arXiv2024

Shortcuts of freely relaxing systems using equilibrium physical observables

Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to shorten the time needed to cool down (or heat up) a system. Though, a strategy to design these effects in mesoscopic systems is missing. We bring forward a description that allows us to formulate such strategies, and, along the way, makes natural these paradoxical behaviors. In particular, we study the evolution of macroscopic physical observables of systems freely relaxing under the influence of one or two instantaneous thermal quenches. The two crucial ingredients in our approach are timescale separation and a nonmonotonic temperature evolution of an important state function. We argue that both are generic features near a first-order transition. Our theory is exemplified with the one-dimensional Ising model in a magnetic field using analytic results and numerical experiments.

cond-mat.stat-mech↗

arXiv2024

The QISG suite: high-performance codes for studying Quantum Ising Spin Glasses

We release a set of GPU programs for the study of the Quantum ($S=1/2$) Spin Glass on a square lattice, with binary couplings. The library contains two main codes: MCQSG (that carries out Monte Carlo simulations using both the Metropolis and the Parallel Tempering algorithms, for the problem formulated in the Trotter-Suzuki approximation), and EDQSG (that obtains the extremal eigenvalues of the Transfer Matrix using the Lanczos algorithm). EDQSG has allowed us to diagonalize transfer matrices with size up to $2^{36}\times2^{36}$. From its side, MCQSG running on four NVIDIA A100 cards delivers a sub-picosecond time per spin-update, a performance that is competitive with dedicated hardware. We include as well in our library GPU programs for the analysis of the spin configurations generated by MCQSG. Finally, we provide two auxiliary codes: the first generates the lookup tables employed by the random number generator of MCQSG; the second one simplifies the execution of multiple runs using different input data.

physics.comp-ph↗

arXiv2023

The Quantum Transition of the Two-Dimensional Ising Spin Glass: A Tale of Two Gaps

Quantum annealers are commercial devices aiming to solve very hard computational problems named spin glasses. Just like in metallurgic annealing one slowly cools a ferrous metal, quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. The field removal diminishes quantum fluctuations but forces the system to traverse the critical point that separates the disordered phase (at large fields) from the spin-glass phase (at small fields). A full understanding of this phase transition is still missing. A debated, crucial question regards the closing of the energy gap separating the ground state from the first excited state. All hopes of achieving an exponential speed-up, as compared to classical computers, rest on the assumption that the gap will close algebraically with the number of qspins, but renormalization group calculations predict that the closing will be instead exponential. Here we solve this debate through extreme-scale numerical simulations, finding that both parties grasped parts of the truth. While the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. Since this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the Quantum Annealing paradigm.

cond-mat.dis-nn↗

arXiv2021

Slow growth of magnetic domains helps fast evolution routes for out-of-equilibrium dynamics

Cooling and heating faster a system is a crucial problem in science, technology and industry. Indeed, choosing the best thermal protocol to reach a desired temperature or energy is not a trivial task. Noticeably, we find that the phase transitions may speed up thermalization in systems where there are no conserved quantities. In particular, we show that the slow growth of magnetic domains shortens the overall time that the system takes to reach a final desired state. To prove that statement, we use intensive numerical simulations of a prototypical many-body system, namely the 2D Ising model.

cond-mat.stat-mech↗