Open research questions in Theoretical and Computational Physics
106 gap statements mined from Theoretical and Computational Physics papers in our 4.5M-paper local library, which holds 559 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.
Choosing where to publish on Theoretical and Computational Physics? See the ranked Physics journals.
What the literature leaves open
The paper does not attempt to select the correct physical solution in the presence of shocks or discontinuities. The simulations are limited to a large but finite number of realizations.
The study is limited to Monte Carlo simulations. The system size is relatively small (L = 20). The disorder is introduced through nonmagnetic impurities or random magnetic fields, which may not be representative of all types of disorder.
The study of disorder effects in Ising metamagnetic phase transition is limited. The understanding of the behavior of the staggered magnetization and susceptibility in the presence of disorder is incomplete.
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.
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.
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.
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 · DOIThe theory is limited to classical N-body systems. The scale separation is required for the mesoscopic free energy to be a good approximation. Long-range interactions require special treatment.
Perturbation Theory of the Free Energy via the Mesoscopic Combined Partition Function · 2026The mean-field approximation has limitations. The study must account for the lack of particle-hole symmetry.
Charge order on a triangular lattice with Mott physics and arbitrary charge density · 2026The study is limited to the extended Hubbard model with nearest-neighbor interaction. The mean-field approximation is an exact approximation only in the limit of infinite coordination number. The study does not account for spatial correlations and magnetic orderings.
Charge order on a triangular lattice with Mott physics and arbitrary charge density · 2026Although 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 · 2026While a rigorous proof remains elusive, the conjecture has been extensively verified using multiple independent methods. Following the approach of, we compute the modular S-transformation of the trace of zero modes for arbitrary fields.
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.
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.
The paper suggests studying the dynamics of non-reversible Monte Carlo algorithms in two or more dimensions with multiple agents. The paper suggests applying the results to other fields, such as repelling chemotaxis.
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.
The development of a theory that can treat long-range interactions. The application of the theory to systems without scale separation. The extension of the theory to other types of systems.
Perturbation Theory of the Free Energy via the Mesoscopic Combined Partition Function · 2026A 7→ Ak is not yet defined, but the roadmap towards the proof of Proposition 4.
Lattice random-field Widom--Rowlinson models · 2026The nature of critical droplets in short-range spin glasses is not well-understood. The behavior of the flexibility in a GSP as a coupling passes through its critical value is not well-studied. The relationship between the metastate and the spin glass phase at low temperatures is not well-established.
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.
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.
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.
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.
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.
The conditional convergence of the lattice series for the electrostatic potential in periodic systems. The limitations of the Ewald method for computing electrostatic potentials.
Most-cited papers in Theoretical and Computational Physics
- Early-warning signals for critical transitions · Nature · 2009 · 4,188 citations
- Application of the lattice Green’s function for calculating the resistance of an infinite network of resistors · American Journal of Physics · 2000 · 239 citations
- A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling · American Journal of Physics · 2004 · 233 citations
- Phase transitions and the search problem · Artificial Intelligence · 1996 · 154 citations
- Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions · American Journal of Physics · 1977 · 153 citations
- The Weber–Morris model in water contaminant adsorption: Shattering long-standing misconceptions · Journal of environmental chemical engineering · 2025 · 126 citations
- Geometric frustration of Jahn–Teller order in the infinite-layer lattice · Nature · 2023 · 120 citations
- TETRATIC PHASE IN THE PLANAR HARD SQUARE SYSTEM? · Computational Methods in Science and Technology · 2004 · 110 citations
- The TSP phase transition · Artificial Intelligence · 1996 · 91 citations
- Teaching the renormalization group · American Journal of Physics · 1978 · 78 citations
Most recent work
- A physics-based fractal model for the permeability-formation factor relation in porous media · International Journal of Heat and Mass Transfer · 2026
- Taylor series perspective on ab initio path integral Monte Carlo simulations with Fermi-Dirac statistics · Physical Review Research · 2026
- Implementation of the hybrid exchange-correlation functionals in the siesta code · Computer Physics Communications · 2026
- Breakdown of Emergent Chiral Order and Defect Chaos in Nonreciprocal Flocks · Physical Review Letters · 2026
- Signs of nonmonotonic finite-volume corrections to g A · Physical Review C · 2026
- Formation of clusters and coarsening in weakly interacting diffusions · Nonlinearity · 2026
- Dynamic models for two nonreciprocally coupled fields: A microscopic derivation for zero, one, and two conservation laws · SciPost Physics · 2026
- A strong-weak duality for the 1d long-range Ising model · SciPost Physics · 2026
- Comment on ‘Properties and dynamics of generalized squeezed states’ · New Journal of Physics · 2026
- Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory · Communications Physics · 2026
Find a gap in your own Theoretical and Computational Physics sub-topic
This page shows what the Theoretical and Computational Physics literature already flags as unresolved. To narrow it to your specific question, search the Research Gap Finder: the search is free with a free account and lists the papers closest to your topic first. Unlocking that topic (50 credits, charged once) fills the comparison table from our 4.5M-paper local library and writes the gaps from its rows.
Open the Research Gap Finder →