Ising-like transitions in the O(nn) loop model on the square lattice

We explore the phase diagram of the O($n$) loop model on the square lattice in the $(x,n)$ plane, where $x$ is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For $n>>2$ we find Ising-like phase transitions associated with the onset of a checkerboard-like ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of $n$ represents a softening of its particle-particle potentials. We also determine critical points in the range $-2\leq n\leq 2$. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the $n>2$ transition may continue into the dense phase of the $n \leq 2$ loop model, or continue as a line of $n \leq 2$ O($n$) multicritical points

Special transitions in an O(nn) loop model with an Ising-like constraint

We investigate the O($n$) nonintersecting loop model on the square lattice under the constraint that the loops consist of ninety-degree bends only. The model is governed by the loop weight $n$, a weight $x$ for each vertex of the lattice visited once by a loop, and a weight $z$ for each vertex visited twice by a loop. We explore the $(x,z)$ phase diagram for some values of $n$. For $0<n<1$, the diagram has the same topology as the generic O($n$) phase diagram with $n<2$, with a first-order line when $z$ starts to dominate, and an O($n$)-like transition when $x$ starts to dominate. Both lines meet in an exactly solved higher critical point. For $n>1$, the O($n$)-like transition line appears to be absent. Thus, for $z=0$, the $(n,x)$ phase diagram displays a line of phase transitions for $n\le 1$. The line ends at $n=1$ in an infinite-order transition. We determine the conformal anomaly and the critical exponents along this line. These results agree accurately with a recent proposal for the universal classification of this type of model, at least in most of the range $-1 \leq n \leq 1$. We also determine the exponent describing crossover to the generic O($n$) universality class, by introducing topological defects associated with the introduction of `straight' vertices violating the ninety-degree-bend rule. These results are obtained by means of transfer-matrix calculations and finite-size scaling.Comment: 19 pages, 11 figure

A Covert Data Transport Protocol

Both enterprise and national firewalls filter network connections. For data forensics and botnet removal applications, it is important to establish the information source. In this paper, we describe a data transport layer which allows a client to transfer encrypted data that provides no discernible information regarding the data source. We use a domain generation algorithm (DGA) to encode AES encrypted data into domain names that current tools are unable to reliably differentiate from valid domain names. The domain names are registered using (free) dynamic DNS services. The data transmission format is not vulnerable to Deep Packet Inspection (DPI).Comment: 8 pages, 10 figures, conferenc

Alkyl-Alkyl Suzuki Cross-Coupling of Unactivated Secondary Alkyl Chlorides

No such thing as a problem substrate! In a reaction designed specifically for the title substrates C-C coupling with alkyl boranes occurred in good yield at room temperature with commercially available catalyst components (see scheme). This versatile method is also suitable for Suzuki reactions of secondary and primary alkyl bromides and iodides, as well as primary alkyl chlorides.National Institute of General Medical Sciences (U.S.) (Grant R01-GM62871)Eli Lilly and Company (Fellowship)Martin Family Society of Fellows for Sustainability (Fellowship)Merck Research LaboratoriesNovartis (Firm

Alkyl-Alkyl Suzuki Cross-Coupling of Unactivated Secondary Alkyl Chlorides

No such thing as a problem substrate! In a reaction designed specifically for the title substrates C-C coupling with alkyl boranes occurred in good yield at room temperature with commercially available catalyst components (see scheme). This versatile method is also suitable for Suzuki reactions of secondary and primary alkyl bromides and iodides, as well as primary alkyl chlorides