Studying the zeroes of partition functions in the space of complex control parameters allows to understand formally how critical behavior of a many-body system can arise in the thermodynamic limit despite various no-go theorems for finite systems. In this work we propose protocols that can be realized in quantum simulators to measure the location of complex partition function zeroes of classical Ising models. The protocols are solely based on the implementation of simple two-qubit gates, local spin rotations, and projective measurements along two orthogonal quantization axes. Besides presenting numerical simulations of the measurement outcomes for an exemplary classical model, we discuss the effect of projection noise and the feasibility of the implementation on state of the art platforms for quantum simulation.

This paper studies the critical behavior of the 3d classical O(N)(N) model with a boundary. Recently, one of us established that upon treating NN as a continuous variable, there exists a critical value N_c > 2Nc>2 such that for 2 \leq N < N_c2≤N<Nc the model exhibits a new extraordinary-log boundary universality class, if the symmetry preserving interactions on the boundary are enhanced. N_cNc is determined by a ratio of universal amplitudes in the normal universality class, where instead a symmetry breaking field is applied on the boundary. We study the normal universality class using the numerical conformal bootstrap. We find truncated solutions to the crossing equation that indicate N_c \approx 5Nc≈5. Additionally, we use semi-definite programming to place rigorous bounds on the boundary CFT data of interest to conclude that N_c > 3Nc>3, under a certain positivity assumption which we check in various perturbative limits.

Lenses in laparoscopes, arthroscopes, and laryngoscopes fog during closed body surgery due to humidity from bodily fluids and differences between body and operating room temperatures.1,2 Surgeons must repeatedly remove, clean, and reinsert scopes that are obscured by fog. As a result, surgery duration, infection risks, and scarring from air exposure increase.3,4 Current methods to address fogging introduce other complications. Acidic alcohol-based coatings scar tissue and quickly evaporate, and heated lenses require reheating every 5 to 20 minutes.3,4 This paper presents a new super-hydrophilic, biocompatible, non-toxic, pH neutral (7.2-7.4), and long-lasting anti-fog coating called VitreOx™.5-7 VitreOx™ can be used wet or dry, without use of alcohol, heat, or fluid evacuation. When applied as a liquid, it easily espouses lenses’ surfaces and edges, and dries within seconds to form a permanently super-hydrophilic surface on silica and polymer surfaces. VitreOx™ avoids current shortfalls by eliminating frequent reapplications, avoiding reapplication for surgeries lasting up to 72 hours.VitreOx™'s anti-fog properties can be explained by nucleation and growth theory for thin films condensation: 1) 3-D droplets, resulting in fogging; 2) 2-D sheets resulting in a flat transparent film; or 3) mixed 3-D on 2-D, resulting in optical distortion. On hydrophobic surfaces (e.g. lenses), condensation occurs with fogging via spherical 3-D droplets, as in the Volmer-Weber model. 3-D droplets scatter light in all directions through refraction yielding opaque or translucent films (fog). VitreOx™ applied to hydrophobic lenses renders them super-hydrophilic. Similar to the 2-D Frank Van-der-Merwe Growth Mode, condensation with uniform wetting yields transparent 2-D films that do not distort optical images transmission.In vitro and in vivo studies of VitreOx™ were conducted to measure performance and duration of anti-fog effectiveness and bio-compatibility. In vitro tests spanned from 3 to 72 hours over a 3-year range. Side-by-side in vivo gastro-endoscopies were conducted on Yucatan™ swine for 90 minutes using 1) VitreOx™, 2) bare lens, and 3) Covidien Clearify™ surfactant with warmer. VitreOx™ coated lenses did not fog nor need reapplication for 90 minutes, while Covidien Clearify™ lasted 38 minutes without fogging, requiring retreatment. No adverse reaction was observed on swines exposed toVitreOx™, in surgery and 12 months thereafter.

The Sliding Window Secretary Problem allows a window of choices to the Classical Secretary Problem, in which there is the option to choose the previous K choices immediately prior to the current choice. We consider a case of this sequential choice problem in which the interviewer has a finite, known number of choices and can only discern the relative ranks of choices, and in which every permutation of ranks is equally likely. We examine three cases of the problem: (i) the interviewer has one choice to choose the best applicant; (ii) the interviewer has one choice to choose one of the top two applicants; and (iii) the interviewer has two choices to choose the best applicant. The form of the optimal strategy is shown, the probability of winning as a function of the window size is derived, and the limiting behavior is discussed for all three cases.

It was recently found that the classical 3d O(N ) model in the semi-infinite geometry can exhibit an "extraordinary-log" boundary universality class, where the spin-spin correlation function on the boundary falls off as S(x) • S(0) ∼ 1 (log x) q . This universality class exists for a range 2 ≤ N < N c and Monte-Carlo simulations and conformal bootstrap indicate N c > 3. In this work, we extend this result to the 3d O(N ) model in an infinite geometry with a plane defect. We use renormalization group (RG) to show that in this case the extraordinary-log universality class is present for any finite N ≥ 2. We additionally show, in agreement with our RG analysis, that the line of defect fixed points which is present at N = ∞ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections. We study the "central charge" a for the O(N ) model in the boundary and interface geometries and provide a non-trivial detailed check of an a-theorem by Jensen and O'Bannon. Finally, we revisit the problem of the O(N ) model in the semi-infinite geometry. We find evidence that at N = N c the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for N > N c .