Ising Model

Non-Convex Portfolio Optimization via Energy-Based Models: A Comparative Analysis Using the Thermodynamic HypergRaphical Model Library (THRML) for Index Tracking ArXiv ID: 2601.07792 “View on arXiv” Authors: Javier Mancilla, Theodoros D. Bouloumis, Frederic Goguikian Abstract Portfolio optimization under cardinality constraints transforms the classical Markowitz mean-variance problem from a convex quadratic problem into an NP-hard combinatorial optimization problem. This paper introduces a novel approach using THRML (Thermodynamic HypergRaphical Model Library), a JAX-based library for building and sampling probabilistic graphical models that reformulates index tracking as probabilistic inference on an Ising Hamiltonian. Unlike traditional methods that seek a single optimal solution, THRML samples from the Boltzmann distribution of high-quality portfolios using GPU-accelerated block Gibbs sampling, providing natural regularization against overfitting. We implement three key innovations: (1) dynamic coupling strength that scales inversely with market volatility (VIX), adapting diversification pressure to market regimes; (2) rebalanced bias weights prioritizing tracking quality over momentum for index replication; and (3) sector-aware post-processing ensuring institutional-grade diversification. Backtesting on a 100-stock S and P 500 universe from 2023 to 2025 demonstrates that THRML achieves 4.31 percent annualized tracking error versus 5.66 to 6.30 percent for baselines, while simultaneously generating 128.63 percent total return against the index total return of 79.61 percent. The Diebold-Mariano test confirms statistical significance with p less than 0.0001 across all comparisons. These results position energy-based models as a promising paradigm for portfolio construction, bridging statistical mechanics and quantitative finance. ...

Stylized Facts and Their Microscopic Origins: Clustering, Persistence, and Stability in a 2D Ising Framework ArXiv ID: 2512.17925 “View on arXiv” Authors: Hernán Ezequiel Benítez, Claudio Oscar Dorso Abstract The analysis of financial markets using models inspired by statistical physics offers a fruitful approach to understand collective and extreme phenomena [“3, 14, 15”] In this paper, we present a study based on a 2D Ising network model where each spin represents an agent that interacts only with its immediate neighbors plus a term reated to the mean field [“1, 2”]. From this simple formulation, we analyze the formation of spin clusters, their temporal persistence, and the morphological evolution of the system as a function of temperature [“5, 19”]. Furthermore, we introduce the study of the quantity $1/2P\sum_{“i”}|S_{“i”}(t)+S_{“i”}(t+Δt)|$, which measures the absolute overlap between consecutive configurations and quantifies the degree of instantaneous correlation between system states. The results show that both the morphology and persistence of the clusters and the dynamics of the absolute sum can explain universal statistical properties observed in financial markets, known as stylized facts [“2, 12, 18”]: sharp peaks in returns, distributions with heavy tails, and zero autocorrelation. The critical structure of clusters and their reorganization over time thus provide a microscopic mechanism that gives rise to the intermittency and clustered volatility observed in prices [“2, 15”]. ...

Phase Transitions in Financial Markets Using the Ising Model: A Statistical Mechanics Perspective ArXiv ID: 2504.19050 “View on arXiv” Authors: Bruno Giorgio Abstract This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features: volatility clustering, negative skewness, heavy tails, the absence of autocorrelation in returns, and the presence of autocorrelation in absolute returns. A significant portion of the dissertation is dedicated to Ising model-based simulations. Due to the lack of an analytical or deterministic solution, the Monte Carlo method was employed to explore the model’s statistical properties. The results demonstrate that the Ising model is capable of replicating the majority of the statistical features analyzed. ...

Hybrid Quantum Algorithms integrating QAOA, Penalty Dephasing and Zeno Effect for Solving Binary Optimization Problems with Multiple Constraints ArXiv ID: 2305.08056 “View on arXiv” Authors: Unknown Abstract When tackling binary optimization problems using quantum algorithms, the conventional Ising representation and Quantum Approximate Optimization Algorithm (QAOA) encounter difficulties in efficiently handling errors for large-scale problems involving multiple constraints. To address these challenges, this paper presents a hybrid framework that combines the use of standard Ising Hamiltonians to solve a subset of the constraints, while employing non-Ising formulations to represent and address the remaining constraints. The resolution of these non-Ising constraints is achieved through either penalty dephasing or the quantum Zeno effect. This innovative approach leads to a collection of quantum circuits with adaptable structures, depending on the chosen representation for each constraint. Furthermore, this paper introduces a novel technique that utilizes the quantum Zeno effect by frequently measuring the constraint flag, enabling the resolution of any optimization constraint. Theoretical properties of these algorithms are discussed, and their performance in addressing practical aircraft loading problems is highly promising, showcasing significant potential for a wide range of industrial applications. ...