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Open research questions in Theoretical and Computational Physics

66 unresolved questions extracted from the limitations and future-work sections of 245 Theoretical and Computational Physics papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • Investigation of the strongly interacting regime, beyond the many-mode mean-field regime. Exploration of the fate of the lower critical dimension in the presence of strong quantum boson-boson interactions.

    Tunable Lower Critical Fractal Dimension for a Nonequilibrium Phase Transition · 2026 · DOI

  • The study of non-equilibrium phase transitions in driven-dissipative systems is less settled than in equilibrium systems. The understanding of critical behavior in complex systems is incomplete.

    Tunable Lower Critical Fractal Dimension for a Nonequilibrium Phase Transition · 2026 · DOI

  • Further study of the universal properties of (1+1)-dimensional interfaces of (2+1)-dimensional models showing APTs. Investigation of the applications of the scaling theory for the interface height distributions. Exploration of the implications of the findings for the understanding and control of nonequilibrium scale-invariant phenomena.

    Universal interface fluctuations in absorbing-state phase transitions · 2026 · DOI

  • The relationship between absorbing phase transitions and Kardar-Parisi-Zhang growth has remained elusive. There is a lack of understanding of the universal properties of (1+1)-dimensional interfaces of (2+1)-dimensional models showing APTs.

    Universal interface fluctuations in absorbing-state phase transitions · 2026 · DOI

  • Future research should aim to improve the understanding of the roughening transition of an electric flux string in a Z2 lattice gauge theory. The results of the paper can be used as a starting point for further studies. Further research is needed to fully understand the implications of the results.

    Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory · 2026 · DOI

  • The roughening transition of an electric flux string in a Z2 lattice gauge theory is not well understood. The entanglement growth makes it harder to access the roughening transition computationally. The paper identifies a gap in the understanding of the static and dynamical properties of an electric string in the confined and deconfined phases.

    Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory · 2026 · DOI

  • The lack of understanding of critical phenomena on fractal lattices. The need for a systematic study of the effects of fractal geometry on phase transitions.

    Critical phenomena on a 3D fractal with intermediate dimensionality: tensor-network study · 2026 · DOI

  • The KZM has only been applied in systems undergoing a transition towards a spatially ordered phase that remains static in the longtime limit. The many-body nature of DTCs is not well understood. The strong noise limit is not well understood.

    Universality of dissipative discrete time crystal formation · 2026 · DOI

  • A precise value of the critical temperature Tc of the isotropic XY model is still lacking. Investigations on other lattice geometries remain scarce.

    Monte Carlo Study of the Phase Transition of the <i>XY</i> Model on a Diamond Lattice · 2026 · DOI

  • There is a need for a subsystem that models tension, collapse, phase-state behavior, and observer-driven modulation. Existing models do not provide a complete dynamic environment for studying stress propagation and structural reemergence.

    Spider–Geometry Engine: A Radial Tension, Phase-State & Observer-Coherence Subsystem for Carlo Collapse Theory v2 (With Visualiser) · 2026 · DOI

  • Further analysis with higher bond dimensions or alternative methods. Investigation of other fractal lattices and their critical phenomena.

    Critical phenomena on a 3D fractal with intermediate dimensionality: tensor-network study · 2026 · DOI

  • Further analysis of the effects of bias on storage and retrieval performance. Application of the model to machine learning and complex systems.

    Dense Associative Memory with Biased Patterns: A Replica Symmetric Analysis · 2026 · DOI

  • The standard Hopfield model does not account for biased patterns. The effects of bias on storage and retrieval performance are not well understood.

    Dense Associative Memory with Biased Patterns: A Replica Symmetric Analysis · 2026 · DOI

  • Generalized wave equations with source and sink terms (eq. 15) for tunable damping in non-reversible Monte Carlo are proposed conceptually but their application and analysis are not developed.

    Dynamics of a Bricklayer Model: Multi-Walker Realizations of True Self-Avoiding Motion · 2026 · DOI

  • Lattice calculations are limited to finite lattice sizes. The lattice breaks some of the symmetries of the CFT that appear in the critical limit. The study is restricted to 3-point functions of fields with spin.

    Three-point functions in critical loop models · 2026 · DOI

  • Further studies can be done to test the conjecture for other types of fields. The methods can be applied to other models of critical phenomena. The study provides a framework for computing correlation functions in critical loop models.

    Three-point functions in critical loop models · 2026 · DOI

  • Although the functional form of rates under the same LDB has been shown to affect correlation properties in weakly interacting systems, whether it can reshape phase behavior in strongly interacting systems remains unclear.

    Beyond Local Detailed Balance: Microscopic Rates Reshape Nonequilibrium Phase Behavior · 2026

  • The study of glassy behavior in random lasers with different constraints. The exploration of the phase diagram of the model. The application of the results to the design of random lasers.

    Smoothed-cubic spin-glass model of random lasers · 2026 · DOI

  • The lack of a realistic representation of gain saturation in prior models. The need for a framework to study glassy random lasers with self-starting mode-locking. The limitation of prior models to spherical constraints.

    Smoothed-cubic spin-glass model of random lasers · 2026 · DOI

  • Future research could focus on providing a general proof of the proposal. Future research could also focus on studying the implications of the proposal for experimental or numerical studies. Future research could also explore the applications of the proposal to other areas of physics and mathematics.

    Modular properties of $$ {\mathcal{W}}_3 $$ generalised Gibbs ensembles · 2026 · DOI

  • The paper identifies a gap in the understanding of the modular properties of generalized Gibbs ensembles. The gap is the lack of a general understanding of the behavior of these ensembles under modular transformations.

    Modular properties of $$ {\mathcal{W}}_3 $$ generalised Gibbs ensembles · 2026 · DOI

  • To test the validity of the KZM for DTC formation in the strong noise limit. To apply the findings to DTCs found in effectively zero-dimensional systems with all-to-all coupling, such as atoms in a single-mode cavity.

    Universality of dissipative discrete time crystal formation · 2026 · DOI

  • Generalization to velocity-dependent forces. Application of the construction to other non-reciprocal systems. Exploration of the implications of the construction for statistical mechanics and Hamiltonian dynamics.

    Hamiltonian description of non-reciprocal interactions · 2026 · DOI

  • The lack of a conventional energy function for non-reciprocal systems limits the use of analytical and numerical tools. The inability to define a conventional energy function precludes the direct application of Monte-Carlo methods to study non-reciprocal systems.

    Hamiltonian description of non-reciprocal interactions · 2026 · DOI

  • To extend the approach to future developments, such as improving computational efficiency and enabling ab initio calculations. To apply the approach to the computation of the orbital Hessian in periodic systems and to time-dependent density functional theory.

    Model density approach to Ewald summations · 2026 · DOI

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66 open questions have been extracted from the limitations and future-work passages of 245 Theoretical and Computational Physics papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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