Related Experiment Video
Updated: Dec 26, 2025
10:23
Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
Published on: May 8, 2015
12.1K
Computational hardness of spin-glass problems with tile-planted solutions
Dilina Perera1, Firas Hamze2, Jack Raymond2
1Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.
Physical Review. E
|March 15, 2020
Summary
Researchers explored the computational hardness of spin-glass instances using a novel solution-planting method. They found tunable problem hardness and observed transitions linked to magnetic ordering, offering insights into complex system behavior.
Area of Science:
- Condensed Matter Physics
- Computational Physics
- Statistical Mechanics
Background:
- Spin-glass models are crucial for understanding disordered magnetic systems.
- Investigating computational hardness is key to solving complex optimization problems.
- A new tunable and scalable method for generating spin-glass instances has been developed.
Purpose of the Study:
- To investigate the computational hardness of spin-glass instances generated by a novel solution-planting approach.
- To explore the relationship between problem parameters, computational hardness, and thermodynamic properties.
- To identify transitions in hardness and their underlying physical mechanisms.
Main Methods:
- Generation of spin-glass instances on a square lattice using a tunable solution-planting method.
- Employing population annealing Monte Carlo to assess typical hardness across parameter space.
- Utilizing simulated annealing and simulated quantum annealing for corroboration.
- Analyzing thermodynamic properties of the generated spin-glass systems.
Main Results:
- Demonstrated a wide range of tunable computational hardness for the generated spin-glass instances.
- Observed multiple transitions in the hardness phase space.
- Correlated harder samples with magnetic ordering transitions.
- Established a link between sample composition and hardness transitions.
Conclusions:
- The developed solution-planting method allows for controlled tuning of spin-glass instance hardness.
- Computational hardness in these systems is intrinsically linked to magnetic ordering phenomena.
- Understanding these transitions provides insights into the behavior of complex disordered systems.
Related Concept Videos
01:14Castigliano's Theorem: Problem Solving
1.1K
The deflection of a simply supported beam that carries a central point load can be analyzed using structural mechanics principles, particularly by applying Castigliano's theorem. This theorem relates the displacement at the load application point to the partial derivatives of the strain energy in the structure. The simply supported beam with a point load at its center has symmetric reaction forces at the supports, each bearing half of the load. The bending moment at any point along the beam is...
1.1K
01:12Theorems of Pappus and Guldinus: Problem Solving
986
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
986
00:59Biot-Savart Law: Problem-Solving
3.7K
The magnitude and direction of a magnetic field created by a steady current can be calculated using the Biot-Savart law.
Consider a mobile phone battery bank as a source of steady current, which flows through the wire connected between the two. What is the magnitude of the magnetic field created by this current at a field point P?
To estimate the magnitude of the total magnetic field, we first consider a small current element of length dl, at a distance r from the field point. Now the following...
Consider a mobile phone battery bank as a source of steady current, which flows through the wire connected between the two. What is the magnitude of the magnetic field created by this current at a field point P?
To estimate the magnitude of the total magnetic field, we first consider a small current element of length dl, at a distance r from the field point. Now the following...
3.7K
01:13Stability of Equilibrium Configuration: Problem Solving
897
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Problem-solving in the context of the stability of equilibrium configuration...
897
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
47.6K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
47.6K
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
234
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
234