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The $\mathbb{C}{P}^{N\ensuremath{-}1}$ sigma model at finite temperature is studied using lattice Monte Carlo simulations on ${S}_{s}^{1}\ifmmode\times\else\texttimes\fi{}{S}_{\ensuremath{\tau}}^{1}$ with circumferences ${L}_{s}$ and ${L}_{\ensuremath{\tau}}$, respectively, where the ratio of the circumferences is taken to be sufficiently large (${L}_{s}/{L}_{\ensuremath{\tau}}\ensuremath{\gg}1$) to approximate the model on $\mathbb{R}\ifmmode\times\else\texttimes\fi{}{S}^{1}$. We show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as ${L}_{\ensuremath{\tau}}$ is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. We find that the global $\mathrm{PSU}(N)=\mathrm{SU}(N)/{\mathbb{Z}}_{N}$ symmetry remains unbroken in different manners for small and large ${L}_{\ensuremath{\tau}}$, respectively: in the small ${L}_{\ensuremath{\tau}}$ region for finite $N$, the order parameter fluctuates extensively with its expectation value consistent with zero after taking an ensemble average, while in the large ${L}_{\ensuremath{\tau}}$ region the order parameter remains small with little fluctuations. We also calculate the thermal entropy and find that the degrees of freedom in the small ${L}_{\ensuremath{\tau}}$ regime are consistent with $N\ensuremath{-}1$ free complex scalar fields, thereby indicating a good agreement with the prediction from the large-$N$ study for small ${L}_{\ensuremath{\tau}}$.

Using the lattice Monte Carlo method, we compute the energy and Tan's contact in the ground state as well as the first excited state of few- to many-fermion systems in a one-dimensional periodic box. We focus on unpolarized systems of N=4,6,...,12 particles, with a zero-range interaction, and a wide range of attractive couplings. In addition, we provide extrapolations to the infinite-volume and thermodynamic limits., 8 pages, 12 figures; published version

We present finite-temperature, lattice Monte Carlo calculations of the particle number density, compressibility, pressure, and Tan's contact of an unpolarized system of short-range, attractively interacting spin-1/2 fermions in one spatial dimension, i.e., the Gaudin-Yang model. In addition, we compute the second-order virial coefficients for the pressure and the contact, both of which are in excellent agreement with the lattice results in the low-fugacity regime. Our calculations yield universal predictions for ultracold atomic systems with broad resonances in highly constrained traps. We cover a wide range of couplings and temperatures and find results that support the existence of a strong-coupling regime in which the thermodynamics of the system is markedly different from the noninteracting case. We compare and contrast our results with identical systems in higher dimensions., Comment: 6 pages, 7 figures; improved, published version

Perturbative calculations suggest that the electroweak phase transition in the minimal supersymmetric standard model (MSSM) can be strong enough for baryogenesis for Higgs masses up to ${m}_{H}\ensuremath{\sim}105$ GeV, provided that the lightest stop mass is in the range 100--160 GeV. We have performed large-scale lattice Monte Carlo simulations of the MSSM electroweak phase transition. We find that the transition is in fact stronger than in perturbation theory. This guarantees that the perturbative mass bounds are conservative ones, and provides a strong motivation for further studies of MSSM baryogenesis.

The mass and interactions of a quantum 't Hooft-Polyakov monopole are measured nonperturbatively using correlation functions in lattice Monte Carlo simulations. A method of measuring the form factors for interactions between the monopole and fundamental particles, such as the photon, is demonstrated. These quantities are potentially of experimental relevance in searches for magnetic monopoles., 11 pages, 6 figures; v2: minor changes to introduction and conclusions, published in PRD

We implement a simple, continuous, analytical model for exciton hopping in an energetically disordered molecular landscape. The model is parameterized against atomistic and lattice Monte Carlo simulations based on quantum-chemical calculations. It captures the essential physics of exciton diffusion in disordered media at different temperatures and yields a universal scaling law of the diffusion length with the dimensionless disorder parameter given by the ratio of the energetic disorder width to the thermal energy.

Results of Monte Carlo simulations of folding of a model ``protein,'' which is a freely joined 27-monomer chain on a simple cubic lattice with nearest-neighbor interactions, are reported. All compact self-avoiding conformations on this chain have been enumerated, and the conformation (``native'') corresponding to the global minimum of energy is known for each sequence. Only one out of thirty sequences folds and finds the global minimum. For this sequence, the folding process has a two-stage character, with a rapid noncooperative compactization followed by a slower transition over a free-energy barrier to the global minimum. The evolutionary implications of the results are discussed.

Short-range order (SRO) in Fe-rich Fe-Cr alloys is investigated by means of atomistic off-lattice Monte Carlo simulations in the semi-grand canonical ensemble using classical interatomic potentials. The SRO parameter defined by Cowley [Phys. Rev. B 77, 669 (1950)] is used to quantify the degree of ordering. In agreement with experiments a strong ordering tendency in the Cr distribution at low Cr concentrations (~< 5%) is observed, as manifested in negative values of the SRO parameters. For intermediate Cr concentrations (5% ~< c_Cr ~< 15%) the SRO parameter for the alpha-phase goes through a minimum, but at the solubility limit the alpha-phase still displays a rather strong SRO. In thermodynamic equilibrium for concentrations within the two-phase region the SRO parameter measured over the entire sample therefore comprises the contributions from both the alpha and alpha-prime phases. If both of these contributions are taken into account, it is possible to quantitatively reproduce the experimental results and interpret their physical implications. It is thereby shown that the inversion of the SRO observed experimentally is due to the formation of stable (supercritical) alpha-prime precipitates. It is not related to the loss of SRO in the alpha-phase or to the presence of unstable (subcritical) Cr precipitates in the alpha-phase., 9 pages, 8 figures

The relativistic correction to the QCD static interquark potential at O(1/m) is investigated nonperturbatively for the first time by using lattice Monte Carlo QCD simulations. The correction is found to be comparable with the Coulombic term of the static potential when applied to charmonium, and amounts to one-fourth of the Coulombic term for bottomonium.

During epitaxial growth of Ge on Si~001!, intermixing can occur between the deposited Ge and the Si substrate. We show that although Ge prefers to wet the surface, entropy drives some fraction into the underlying layers. We present a simple model of intermixing by equilibration of the top crystal layers in the absence of bulk diffusion. The equilibration is performed with a flexible lattice Monte Carlo simulation. Ultimately, intermixing leads to a temperature-dependent graded Ge concentration. The resulting evolution of chemical potential is consistent with the onset of islanding after 3‐ 4 monolayers of deposition.

A lattice Monte Carlo model is proposed for quantifying the dispersion of DNA during microfluidic electrophoresis in a quasiperiodic array of posts similar to that encountered in the microfluidic self-assembly of magnetic bead columns. The transport model is semiphenomenological in the sense that all parameters, such as the post geometry, average collision time, and collision probability, are assumed to be accessible either directly from experiment or from a model of the microscale physics. Asymptotically exact formulas are obtained for the mean velocity and dispersivity using Taylor-Aris dispersion theory, which permits a straightforward analysis of the separation efficiency. The model is applicable to a variety of situations involving collision-retardation processes.