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arXiv:2508.08154 · Physical review. B./Physical review. B

Spin-liquid and spin-glass behavior in quantum spin models with all-to-all p -spin interactions

Shusei Wadashima, Yukitoshi Motome

Published Nov 4, 2025• 0 citations
arXivHTMLPDF

Abstract

Spin-liquid and spin-glass states represent two distinct phases of disordered quantum spin systems. These states are, in principle, distinguished by quantum-entangled fluctuations and spin freezing, but identifying each state and characterizing the transition between them remains challenging. Here, we systematically explore the relationship between the spin-liquid and spin-glass states using a model with all-to-all random interactions among $p$ spins, which interpolates between the Ising-like one-component, XY-like two-component, and isotropic three-component cases. By analyzing the system-size $N$ dependence of the Edwards-Anderson order parameter and the density of states, we identify the transition from the spin liquid to the spin glass for various values of $p$. We show that the phase diagrams for different $p$ can be unified through a scaling with $N/{p}^{2}$, revealing that increasing anisotropy in the interactions systematically suppresses the spin-liquid phase and extends the spin-glass regime. Furthermore, we examine the competition between multiple-spin interactions and anisotropy under an external magnetic field in the isotropic case, and find that the spin-liquid phase transitions into the spin-glass phase before entering a quantum paramagnetic phase. Our findings provide insights into quantum disordered phases and the transitions between them.

DOI
10.1103/r5d6-2cby

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Spin-liquid and spin-glass states represent two distinct phases of disordered quantum spin systems. These states are, in principle, distinguished by quantum-entangled fluctuations and spin freezing, but identifying each state and characterizing the transition between them remains challenging. Here, we systematically explore the relationship between the spin-liquid and spin-glass states using a model with all-to-all random interactions among ppp spins, which interpolates between the Ising-like one-component, XY-like two-component, and isotropic three-component cases. By analyzing the system-size NNN dependence of the Edwards-Anderson order parameter and the density of states, we identify the transition from the spin liquid to the spin glass for various values of ppp. We show that the phase diagrams for different ppp can be unified through a scaling with N/p2N/{p}^{2}N/p2, revealing that increasing anisotropy in the interactions systematically suppresses the spin-liquid phase and extends the spin-glass regime. Furthermore, we examine the competition between multiple-spin interactions and anisotropy under an external magnetic field in the isotropic case, and find that the spin-liquid phase transitions into the spin-glass phase before entering a quantum paramagnetic phase. Our findings provide insights into quantum disordered phases and the transitions between them.
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Spin-glass (SG) is a fascinating system that has garnered significant attention due to its intriguing properties and implications for various research fields. One of the key characteristics of spin glasses is that they contain random disorder, which leads to many possible states of the system occurring with very close probabilities. We explore the concept of spin-glass superposition states (SSs), which are equiprobable SSs of possible electronic configurations. Using the Edward-Anderson (EA) type SG order parameter qEAq_{EA}qEA​ and magnetization, we demonstrate that these SSs can be classified based on their contribution to distinguishing magnetic order (disorder), such as SG, (anti)ferromagnetic (FM), and paramagnetic (PM) phases. We also generalize these superposition states based on the system size and investigate the entanglement of these phase-based SSs using the negativity measure. We show that the SG order parameter can be utilized to determine the entanglement of magnetically ordered (disordered) phases, or vice versa, with negativity signifying magnetic order. Our findings provide further insight into the nature of quantum SSs and their relevance to SGs and quantum magnets. They have implications for various fields, including condensed matter physics, where SGs are a prototypical example of disordered systems. They are also relevant for other fields, such as neural networks, optimization problems, and information storage, where complex systems with random disorder behavior are greatly interested. Overall, our study provides a deeper understanding of the behavior of SGs and the nature of quantum SSs, with potential applications in various fields.
We propose that spin glasses can exist in equally probable superposition states (SSs) comprising potential configurations. Employing the Edward-Anderson (EA) order parameter and magnetization, we establish a classification scheme for these SSs based on their contribution to discerning magnetic order (disorder), such as SG, ferromagnetic (FM), and paramagnetic (PM) phases. We also encompass various system sizes and investigate the entanglement properties of these phase-dependent SSs using the negativity measure. Our analysis reveals that the SG order parameter can be employed to determine the entanglement characteristics of magnetically ordered (disordered) phases, and vice versa, with negativity indicating the presence of magnetic order. Specifically, we examine the relationship between negativity and susceptibility in spin-glass systems. Our findings provide further insight into the role of quantum superposition in spin glasses and quantum magnets.
In this work we study the effects of quantum fluctuations in a disordered magnetic system. We consider a cluster-spin Ising model with antiferromagnetic short range interactions (J0) and disordered long range interactions (J) between clusters, where the system is under the influence of a transverse magnetic field Γ. The analytic treatment of the model is done by the replica method and Trotter formalism, in which a cluster mean field, replica symmetric and static approximations are used. This allows us to obtain an effective model of a single cluster that is exactly diagonalized. Thermodynamic quantities like order parameter and free energy are obtained then, the phase diagrams are analyzed. They are shown in temperature versus J0=J phase diagrams for some intensities of Γ. With Γ = 0, when we decrease the temperature (for lower intensities of J0=J) a continuous phase transition between the paramagnetic and cluster spin glass state (CSG) is found. When we increase the ratio J0=J, the system presents the antiferromagnetic phase (AF). The CSG state and the AF phase are separated by first order transitions. In the intermediate region of disorder, there exist a small interval in the AF-PM transition that is first order. When Γ is increased, the transitions PM-AF and PM-VSC decrease toward critical points in the lower and higher disorder, respectively. It is worth to note, in the intermediate range of disorder, that the transition CSG-AF disappears, letting a PM phase between them, even for zero temperature. Besides that, the first-order region, in the PM-AF transition, turns into a second order phase transition, changing its criticality in the low temperature regime. Our results show that quantum fluctuations affects the phase transitions of the model being capable to suppress and/or change his criticality. The present work suggests a model and a mechanism of the change in the criticality away from the quantum critical point, helping the investigation of this interesting and recent topic.
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