Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$ vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^m$, where $m$ denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for $N_{Z,G,j}$ for arbitrary $L_y$. We also present plots of zeros of the partition function in the $q$ plane for various values of $v$ and in the $v$ plane for various values of $q$. Explicit results for partition functions are given in the text for $L_y=2,3$ (free) and $L_y=4$ (cylindrical), and plots of partition function zeros are given for $L_y$ up to 5 (free) and $L_y=6$ (cylindrical). Plots of the internal energy and specific heat per site for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file

Little Higgs Models and Precision Electroweak Data

We study the low energy limit of Little Higgs models. The method consists in eliminating the heavy fields using their classical equations of motion in the infinite mass limit. After the elimination of the heavy degrees of freedom we can directly read off deviations from the precision electroweak data. We also examine the effects on the low energy precision experiments.Comment: Misprint in eps3 for the custodial model corrected and additional discussion of the triplet higg

The g-2 of the Muon in Localized Gravity Models

The (g-2) of the muon is well known to be an important model building constraint on theories beyond the Standard Model. In this paper, we examine the contributions to $(g-2)_\mu$ arising in the Randall-Sundrum model of localized gravity for the case where the Standard Model gauge fields and fermions are both in the bulk. Using the current experimental world average measurement for $(g-2)_\mu$, we find that strong constraints can be placed on the mass of the lightest gauge Kaluza-Klein excitation for a narrow part of the allowed range of the assumed universal 5-dimensional fermion mass parameter, $\nu$. However, employing both perturbativity and fine-tuning constraints we find that we can further restrict the allowed range of the parameter $\nu$ to only one fourth of its previous size. The scenario with the SM in the RS bulk is thus tightly constrained, being viable for only a small region of the parameter space.Comment: 16 pages, 2 figs, LaTex, Additional discussion adde

Potts model on recursive lattices: some new exact results

We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in the text). We also get the exact solution for strips of the Kagome lattice for widths $L_y=2,3,4,5$. As further examples we consider two lattices with different type of regular symmetry: a strip with alternating layers of width $L_y=3$ and $L_y=m+2$, and a strip with variable width. Finally we make some remarks on the Fisher zeros for the Kagome lattice and their large q-limit.Comment: 17 pages, 19 figures. v2 typos corrected, title changed and references, acknowledgements and two further original examples added. v3 one further example added. v4 final versio

A Tight Karp-Lipton Collapse Result in Bounded Arithmetic

Cook and Krajíček [9] have obtained the following Karp-Lipton result in bounded arithmetic: if the theory proves , then collapses to , and this collapse is provable in . Here we show the converse implication, thus answering an open question from [9]. We obtain this result by formalizing in a hard/easy argument of Buhrman, Chang, and Fortnow [3]. In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajíček [9]. In particular, we obtain several optimal and even p-optimal proof systems using advice. We further show that these p-optimal systems are equivalent to natural extensions of Frege systems

Singlet Fermionic Dark Matter explains DAMA signal

It has been suggested that, considering channeling effect, the order of a few GeV dark matters which are elastically scattered from detector nuclei might be plausible candidates reconciling the DAMA annual modulation signal with the results of other null experiments. We show that Singlet Fermionic Dark Matter can be such a dark matter candidate, simultaneously providing the correct thermal relic density which is consistent with the WMAP data.Comment: 9 pages, 3 figure

New Higgs signals induced by mirror fermion mixing effects

We study the conditions under which flavor violation arises in scalar-fermion interactions, as a result of the mixing phenomena between the standard model and exotic fermions. Phenomenological consequences are discussed within the specific context of a left-right model where these additional fermions have mirror properties under the new SU(2)_R gauge group. Bounds on the parameters of the model are obtained from LFV processes; these results are then used to study the LFV Higgs decays (H --> tau l_j, l_j = e, mu), which reach branching ratios that could be detected at future colliders.Comment: 12 pages, 2 figures, ReVTex4, graphicx, to be published in Phys. Rev.

Controlling dipole-dipole frequency shifts in a lattice-based optical atomic clock

Motivated by the ideas of using cold alkaline earth atoms trapped in an optical lattice for realization of optical atomic clocks, we investigate theoretically the perturbative effects of atom-atom interactions on a clock transition frequency. These interactions are mediated by the dipole fields associated with the optically excited atoms. We predict resonance-like features in the frequency shifts when constructive interference among atomic dipoles occur. We theoretically demonstrate that by fine-tuning the coherent dipole-dipole couplings in appropriately designed lattice geometries, the undesirable frequency shifts can be greatly suppressed.Comment: 14 pages, 4 figure

A "Littlest Higgs" Model with Custodial SU(2) Symmetry

In this note, a ``littlest higgs'' model is presented which has an approximate custodial SU(2) symmetry. The model is based on the coset space $SO(9)/(SO(5)\times SO(4))$. The light pseudo-goldstone bosons of the theory include a {\it single} higgs doublet below a TeV and a set of three $SU(2)_W$ triplets and an electroweak singlet in the TeV range. All of these scalars obtain approximately custodial SU(2) preserving vacuum expectation values. This model addresses a defect in the earlier $SO(5)\times SU(2)\times U(1)$ moose model, with the only extra complication being an extended top sector. Some of the precision electroweak observables are computed and do not deviate appreciably from Standard Model predictions. In an S-T oblique analysis, the dominant non-Standard Model contributions are the extended top sector and higgs doublet contributions. In conclusion, a wide range of higgs masses is allowed in a large region of parameter space consistent with naturalness, where large higgs masses requires some mild custodial SU(2) violation from the extended top sector.Comment: 22 pages + 8 figures; JHEP style, added references and extra discussion on size of T contributions, as well as some other minor clarifications. Version to appear in JHE

Mass matrix Ansatz and lepton flavor violation in the THDM-III

Predictive Higgs-fermion couplings can be obtained when a specific texture for the fermion mass matrices is included in the general two-Higgs doublet model. We derive the form of these couplings in the charged lepton sector using a Hermitian mass matrix Ansatz with four-texture zeros. The presence of unconstrained phases in the vertices phi-li-lj modifies the pattern of flavor-violating Higgs interactions. Bounds on the model parameters are obtained from present limits on rare lepton flavor violating processes, which could be extended further by the search for the decay tau -> mu mu mu and mu-e conversion at future experiments. The signal from Higgs boson decays phi -> tau mu could be searched at the large hadron collider (LHC), while e-mu transitions could produce a detectable signal at a future e mu-collider, through the reaction e mu -> h0 -> tau tau.Comment: 17 pages, 9 figure