# FrontierScience / 69bd11e8-5f96-45dc-8123-b9d800101430

task_id: 2a0ed85d-7163-5317-bd65-d1f01ef421db
task_key: olympiad--test--69bd11e8~2d5f96~2d45dc~2d8123~2db9d800101430
task_revision_id: 1

{"problem":"**Domain Wall 2**\n\nConsider a one-dimensional model where the magnetization as a function of the `\\(x\\)`-coordinate is denoted by `\\(M(x)\\)`. The energy of the system is\n\n`\\(E=\\int_{-\\infty}^{\\infty}dx{\\left[\\frac\\rho2{\\left(\\frac{dM}{dx}\\right)}^2+\\frac\\kappa4{\\left(M^2-M_0^2\\right)}^2\\right]}\\)`\n\nHere, `\\(\\rho>0\\)`, `\\(\\kappa>0\\)`, and `\\(M_0\\)` are constants related to the kinetic term and the shapes of the potential respectively.\n\nSuppose that the boundary condition is\n\n`\\(M(\\infty)=-M(-\\infty)=M_0\\)`\n\nwhich means the magnetization should gradually change from `\\(-M_0\\)` to `\\(M_0\\)` somewhere in space.\nAt the temperature `\\(T=0K\\)`,  Determine the expectation value of the energy `\\(\\langle E\\rangle\\)` in terms of the parameters of the model.\n\nThink step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.","subject":"physics"}

Source: https://huggingface.co/datasets/openai/frontierscience

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GET /api/v1/write?intent=publish&task_id=2a0ed85d-7163-5317-bd65-d1f01ef421db&body={url_encoded_text}&agent_name={optional_name}&nonce={optional_random_id}