# Questions tagged [disorder]

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### What are twisted boundary conditions?

What is the physical intution behind "twisted" boundary conditions (TBC), in what kind situations does one employ TBC? I understand that finite systems, must be modeled with open boundary ...
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### Are complexity and disorder correlated in entropy?

I am coming from the musical field, but I am looking into the topic of entropy. In many articles from the field of physics, I keep finding what I consider a sort of misunderstanding, but I may be ...
54 views

### What is the intuitive meaning of the typical value $e^{\left\langle \log X \right\rangle}$ of a random variable $X$?

The notion of the typical value $e^{\left\langle \log X \right\rangle}$ of a random variable $X$ comes up often in the study of disordered systems. For examples see the short paragraph above eq. (4) ...
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Consider solving a disordered system with Hamiltonian $H[h(x)]$ where $h(x)$ denotes the disorder parameter/random variable at lattice site $x$ (e.g., possibly of independent Gaussian distributions $\... • 1,708 0 votes 1 answer 47 views ### Do annealed energies underestimate quenched energies? In the physics of disordered systems, there are two ways to treat the disorder: Quenched disorder, in which the disordered variables are considered to be frozen with respect to the thermodynamic ... 1 vote 0 answers 58 views ### Quenched and annealed disorder in a combinatorial problem For a research project I'm dealing with a combinatorial problem which I am modeling as a disordered system. For some context, the problem is the TSP, and the disorder enters through the weights on its ... 1 vote 2 answers 47 views ### Question about molecules and their movement This question might be nonsensical and, if it is, please leave a reply so I know and can remove it. I'm currently learning about basic thermodynamics and was thinking, if there is some "average&... • 49 2 votes 0 answers 62 views ### Averaging SYK models and the disappearance of the density matrix In A strongly correlated metal built from Sachdev-Ye-Kitaev models by Song et al. they wish to calculate the generating function for a system with quenched disorder. In the Keldysh formalism, this ... • 283 0 votes 0 answers 23 views ### What is the physical meaning of entropy rate? When I first heard about the notion of "entropy rate", I thought it should be something like a derivative form of entropy. I know what entropy indicates in view of (dis)order. However, after ... • 300 0 votes 0 answers 70 views ### Reading materials on Lee-Yang zeroes for spin systems with quenched disorder I am trying to have a deeper understanding of the Lee-Yang zeros for spin systems with quenched disorder. So far I have read Section 3.2 of Itzykson-Drouffe which covers the concept for Ising model. ... • 360 3 votes 1 answer 114 views ### References for prerequisite material for understanding papers on Generalized Global Symmetries I want to understand the papers https://arxiv.org/abs/1412.5148 and https://arxiv.org/abs/1703.00501. Assuming that I understand basics of gauge theories, could someone suggest some references ... 0 votes 0 answers 36 views ### Derivation of Lyapunov exponent in 1D disordered system What I am considering is a tight-binding model of 1D disordered system. According to the literature (page 1500, equation (60)), Lyapunov exponent$\gamma$is calculated as follows which I am not ... 3 votes 1 answer 137 views ### Weak localization, strong localization, and localization without a metal-insulator transition As I begin to read literature on Anderson localization by disorder, authors are distinguishing between cases that are unfamiliar to me, namely weak localization, strong localization, and localization ... • 521 7 votes 4 answers 908 views ### Why is a symmetric traceless tensor zero when averaged over all directions? In page 168 in Ref. , the authors search for a suitable order parameter for the nematic phase in liquid crystal. If$\vec v^\alpha$is the direction of a single molecule, than due to the inversion ... • 169 6 votes 0 answers 230 views ### Complete localization in 2D The two-dimensional Anderson model is the model $$H = T + \lambda V_\omega$$ where$T$is nearest-neighbor hopping on$\mathbb{Z}^2$and$V_\omega$is a random potential.$\lambda > 0$is the ... • 2,164 5 votes 0 answers 211 views ### Random Fermion Hopping Model Consider a random, all to all, complex fermion hopping model on$N$sites with quenched (Gaussian) disorder, that has a well defined large$N$limit (aka the SYK2 model). So, we start with free ... • 744 2 votes 0 answers 50 views ### De Almeida-Thouless line and spin glass in the Hopfield network From the SK model, the Almeida-Thouless line appears to divide the stable paramagnetic phase and unstable spin-glass phase in the presence of an external magnetic field. However, in the case of a ... 0 votes 1 answer 186 views ### Level statistics of many body localization I was calculating some Hamiltonian's spectrum statistics. Namely, I calculated the Hamiltonian's eigenvalues and sorted them in an ascending order:$E_1,E_2,E_3...E_N$. The quantity I calculated is r, ... • 151 12 votes 2 answers 325 views ### What is the intuition behind the statement that non-equilibrium systems with static disorder are self-averaging? In this paper(1) by C. De Dominics, he makes the argument that in a dynamical statistical mechanics system, one doesn't need to apply the replica trick and can directly disorder average the generating ... • 347 1 vote 0 answers 58 views ### If universe is expanding shouldn't its 'disorderness' decrease? I've came across Clausius Inequality which says that entropy of an isolated system always increases (in an irreversible process). Assuming universe to be an isolated system, a time will come when ... • 616 0 votes 2 answers 267 views ### Calculate an order parameter for a given set of atomic coordinates I have a box which contains a few thousand atoms, and I would like to be able to calculate a single number which gives some indication of how ordered their arrangement is in 3D. For example, if they ... • 111 4 votes 2 answers 323 views ### What is(are) the effect(s) of disorder on electrical conductivity? As a non-specialist, I asked the question "What are disorders in condensed matter parlance?" about the meaning of disorder in condensed matter physics. I also wrote a non-specialist answer after some ... • 24.6k 4 votes 1 answer 363 views ### What are disorders in condensed matter parlance? Condensed matter physicists often use the term disorder. What is a disorder? Is it some point defect or line defect? How are they modelled in a theory? • 24.6k 8 votes 2 answers 921 views ### Why do we disorder-average before/after taking the logarithm of the partition function for annealed/quenched disorder? Pg. 19 of these notes says Crucially, the [disorder] average$\overline{\log Z}$has to be computed after taking the logarithm. Such an average is called quenched ... Computing the average first, ... • 42.6k 4 votes 0 answers 329 views ### Difference between Anderson localization and weak localization I have read that weak localization is a precursor to Anderson localization. Weak localization happens due to the constructive interference between paths that loop around in opposite direction, on ... • 898 1 vote 0 answers 217 views ### Derivation of the gradient expansion of the Keldysh nonlinear sigma model for disorder metals My confusion relates to Appendix C of this this paper although the same derivation is presented in many others. When deriving the gradient expansion of this term arrives at a term quadratic in the ... • 146 -1 votes 1 answer 64 views ### Are maximum order and maximum disorder equally easy to describe? If we have a collection of particles in a maximum ordered state, is this state just as easy to describe as a collection of particles in a minimum ordered state? If we have a collection of particles ... 2 votes 3 answers 2k views ### What does the second law of thermodynamics really mean? I started reading about entropy and the second law of thermodynamics. Different sites give different definitions and meanings of this law. A few of them: Disorder always increases heat always flows ... 2 votes 1 answer 206 views ### Fractal structure in colloidal systems In describing the configuration of a colloidal system, one often deals with either, disordered fluid states, disordered jammed states or crystalline states (so an underlying lattice structure), but in ... • 4,275 7 votes 1 answer 1k views ### Quenched systems - disorder average (SYK model) In a system with quenched disorder one is usually looking for self-averaging quantities, i.e., quantities such that the average over the couplings produces a typical" configuration in the ... • 317 2 votes 0 answers 52 views ### Single-electron propagator in disordered media: higher moments? The known result that the impurity-averaged single electron propagator takes the form$ \langle G_0(r) \rangle \sim e^{-|r|/\ell} $, for$\ell$the mean free path is frequently quoted by papers on ... • 91 2 votes 0 answers 53 views ### Superconductor-insulator transition at finite temperatures I know that it is possible to have a phase transition at$T=0$between a superconductor and an insulator. The mechanism is not the "usual" QPT as the system is not translationally invariant: the ... • 143 0 votes 1 answer 221 views ### Do hydroelectric power plants violate the popular scientific notion of entropy = disorder? I had a discussion yesterday, and I found my understanding of entropy lacking. I know that entropy is not exactly the same as the degree of disorder in a system, but I also know that outside of ... • 2,720 1 vote 1 answer 394 views ### Why does entropy arise from order? Why does entropy arise from order? Thanks. I'm not sure if this question has already been answered on this site. If anyone needs me to clarify the question, please post in the comments and I'll ... • 304 4 votes 2 answers 1k views ### Difference Between Ruderman-Kittel-Kasuya-Yosida (RKKY) Interaction and Kondo Effect The question is in the title. I don't understand the difference between these two effects. Based on my understanding, the Kondo Effect is where the conduction electrons effectively screen a local ... • 121 0 votes 0 answers 62 views ### What is a zero temperature horizon? While reading the paper "Disorder horizons: Holography of randomly disordered fixed points" by Hartnoll and Santos, I came across this: We are interested in solutions with a zero temperature ... • 1,737 0 votes 1 answer 42 views ### Conductance of disordered conductor I'm struggling with a rather advanced problem. Consider a conductor placed between two leads. The conductor is not completely clean but contains all kinds of impurities. The goal is to find the ... • 662 2 votes 1 answer 1k views ### Physical understanding of Anderson (disorder) localisation My current understanding is that waves in disordered potentials experience localisation due to interference effects. (eg an electron in a disordered medium tries to take different paths of effectively ... 1 vote 0 answers 270 views ### Why doesn't entropy get decreased in adiabatic expansion process? I was reading the second step of Carnot cycle in which the system undergoes adiabatic expansion doing work & thus decreasing the internal energy of itself. The entropy didn't change as no further ... 1 vote 0 answers 79 views ### phonon dispersion with random masses In order to see how phonons should be affected by disorder, I've been playing around with a model involving a 1D chain of masses linked by springs, where the spring strengths are all the same but the ... • 378 13 votes 2 answers 1k views ### scaling theory of Anderson localization Initially, Anderson studied the eigenstates of the tight-binding Hamiltonian $$H = \sum_n \epsilon_n a_n^\dagger a_n + V \sum_{m,n} a_m^\dagger a_n .$$ His question was whether the eigenstates ... • 1,119 7 votes 1 answer 329 views ### Why does the diffusion pole universally appear in the two-particle Greens function (diffuson) I've been thinking about the calculation of the diffuson in the context of impurity-averaged Greens functions. If you calculate the two-particle Greens function in the ladder approximation (for ... 3 votes 2 answers 251 views ### Entropy / Structure Relations I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? The further a system is from its maximum ... 0 votes 1 answer 226 views ### Orienational order parameter in isotropic systems I have what may be a dummy question. In NMR or in the study of liquid crystals for example, an order parameter$S$is often used: $$S=\left\langle\frac{1}{2}\left(3\cos^2\theta−1\right)\right\rangle ... • 1 0 votes 1 answer 114 views ### Maximising entropy when energy is shared between systems This is a problem to do with statistical physics, and the exchange of energy when we have two microcanonical ensemble. I don't understand why there should be a minus sign in the middle, if Energy* is ... • 1,199 2 votes 2 answers 109 views ### Modeling a list with a tunable degree of disorder/shuffling Imagine we have a list of ordered numbers L = (1, 2,\dots, N). I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ... • 123 4 votes 1 answer 415 views ### Confusions regarding entropy Help, I am terribly confused about entropy. On the one hand, I am taught at school that a substance such as an ice/solid has a lower entropy than its gaseous equivalent and that a process such as ... • 797 1 vote 2 answers 287 views ### Qualitative discussion about entropy and disorder Many discussions about entropy and disorder use examples of decks of cards, pages of books thrown in the air, two gases being mixed in a container, even the state of a nursery at the end of the day ... 5 votes 2 answers 408 views ### Entropy: two explanations for the same quantity? I studied thermodynamics and I saw the following definition for entropy:$$ \Delta S = \int_1^2 \frac{\text{d}Q}{T}$$that we use to calculate$\Delta S\$ for different types of transformations. In ... 