There is a theoretical and experimental controversy on the possibility for magnetic nanoparticles (MNPs) heated by high-frequency magnetic fields to reach a temperature much larger than the one of their environments. Here the internal temperature of magnetically heated magnetite MNPs is measured using the temperature dependence of their lattice parameter , and compared to the one of their environments, measured from reference non-magnetic particles. Within the uncertainty of our experimental methods, which is estimated to be below 5°C, the MNP temperature is the same as the one of their environments.

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We consider two-dimensional $q$-state quantum clock models with quantum fluctuations connecting states with all-to-all clock transitions with different matrix elements, including the case of transitions restricted to only the nearest clock states. We study the quantum phase transitions in these models with the aim of characterizing the cross-over from emergent U(1) symmetry at the transition (for $q \ge 4$) to $Z_q$ symmetry of the ordered state. As in classical three-dimensional clock models, the cross-over is governed by a dangerously irrelevant operator with scaling dimension $\Delta_q>3$. We specifically study $q=5,6$ models with different forms of the quantum fluctuations and different anisotropies in the classical models. In all cases studied, we find consistency with the expected classical XY critical exponents related to the conventional order parameter as well as the scaling dimensions $\Delta_q$. However, the initial weak violation of the U(1) symmetry in the ordered phase, characterized by an angular $Z_q$ symmetric order parameter $\phi_q$, scales with the system size in an unexpected way. As a function of the system size (length) $L$ in the close neighborhood of the critical temperature, $\phi_q \propto L^p$, where the known value of the exponent is $p=2$ in the classical isotropic XY model. In contrast, for strongly anisotropic XY models and all the quantum models studied, we observe $p=3$. For weakly anisotropic models we observe a cross-over from $p=2$ to $p=3$ scaling. The exponent $p$ also directly impacts the exponent $\nu'$ characterizing the divergence of the U(1)length scale $\xi'$ in the thermodynamic limit, according to the general relationship $\nu'=\nu(1+|y_q|/p)$, where $y_q=3-\Delta_q$ is the scaling dimension of the clock field. We present a phenomenological argument for the $p=3$.

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We use the state-of-the-art tensor network state method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram of spin-$1/2$ $J_1$-$J_2$ Heisenberg model on square lattices up to $24\times 24$. We provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region $0.56\lesssim J_2/J_1\leq0.61$ before the system enters the well known collinear antiferromagnetic phase. We stress that our work gives rise to the first solid PEPS results beyond the well established density matrix renormalization group (DMRG) through one-to-one direct benchmark for small system sizes. Thus it provides us very strong numerical evidences to explicitly demonstrate the conceptual superiority of PEPS over DMRG for large 2D systems. The physical nature of the discovered gapless QSL and potential experimental implications are also addressed.

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We study spectral gaps of the one-dimensional totally asymmetric simple exclusion process (TASEP) with open boundaries in the maximal current phase. Earlier results for the model with periodic boundaries suggest that the gaps contributing to the universal KPZ regime may be understood as points on an infinite genus Riemann surface built from a parametric representation of the cumulant generating function of the current. We perform explicit analytic continuations from the known large deviations of the current for open TASEP, and confirm the results for the gaps by an exact Bethe ansatz calculation, with additional checks using high precision extrapolation numerics.

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